a note on two convergence acceleration methods for ordinary continued fractions abstract in this note we compare two recent methods of convergence acceleration for ordinary continued fractions the first one introduced by thron and waadeland 13 and further developed by brezinski 1 the second one by jacobsen and waadeland 4 5

truncation error bounds for limit periodic continued fractions many special functions of mathematical physics have representations in the form of limit k periodic continued fractions f k 1 b n where limn b n b or lim n b kn i i where k is a positive integer and 0 i k 1 for computation of such functions by continued fractions one needs sharp bounds for the truncation error left f f n right resulting when the value f is replaced by the nth approximate f n in this paper we present bounds for limit 4 periodic continued fractions k 1 bn some of these bounds are shown to be best relative to limited given information

construction for binary asymmetric error correcting codes corresp a construction method of asymmetric error correcting codes is proposed in this method a t fold asymmetric error correcting code of length n 1 is constructed by expurgating and puncturing any t fold symmetric error correcting code of length n these codes are designed for use on binary asymmetric channels such as large scale integration lsi memory protection on which transition is one way

free vibrations of elliptical rings with circumferentially variable thickness abstract this paper deals with the in plane free vibration of rings with a nominally elliptical centreline results are presented for rings of constant axial length that have a rectangular cross section the radial thickness of which is constant or has a simple analytically defined circumferential variation additionally and for the first time the effects of small variations in in plane profile such as those arising in practical rings due to manufacturing tolerances are considered the problem is tackled using an approach in which the true middle surface is determined numerically from the outer and inner surface profiles which can be defined either by exact analytical expressions or in a more general way using fourier series the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a range of cases including some that have previously been studied by other authors and some that have not the effects on frequency splitting due to profile variations and the aspect ratio of the ellipse are emphasized results obtained using the developed numerical approach show excellent agreement with finite element predictions

generalized sphere packing bound kulkarni and kiyavash recently introduced a new method to establish upper bounds on the size of deletion correcting codes this method is based upon tools from hypergraph theory the deletion channel is represented by a hypergraph whose edges are the deletion balls or spheres so that a deletion correcting code becomes a matching in this hypergraph consequently a bound on the size of such a code can be obtained from bounds on the matching number of a hypergraph classical results in hypergraph theory are then invoked to compute an upper bound on the matching number as a solution to a linear programming problem the problem of finding fractional transversals the method by kulkarni and kiyavash can be applied not only for the deletion channel but also for other error channels this paper studies this method in its most general setup first it is shown that if the error channel is regular and symmetric then the upper bound by this method coincides with the well known sphere packing bound and thus is called here the generalized sphere packing bound even though this bound is explicitly given by a linear programming problem finding its exact value may still be a challenging task the art of finding the exact upper bound or slightly weaker ones is the assignment of weights to the hypergraph s vertices in a way that they satisfy the constraints in the linear programming problem in order to simplify the complexity of the linear programming we present a technique based upon graph automorphisms that in many cases significantly reduces the number of variables and constraints in the problem we then apply this method on specific examples of error channels we start with the z channel and show how to exactly find the generalized sphere packing bound for this setup next studied is the nonbinary limited magnitude channel both for symmetric and asymmetric errors where we focus on the single error case we follow up on the deletion channel which was the original motivation of the work by kulkarni and kiyavash and show how to improve upon their upper bounds for single deletion correcting codes since the deletion and grain error channels have a similar structure for a single error we also improve upon the existing upper bounds on single grain error correcting codes finally we apply this method for projective spaces and find its generalized sphere packing bound for the single error case

acceleration of limit periodic continued fractions by the t m transformation we consider limit periodic continued fractions b 0 a 1 1 a n 1 where lim n a n a is finite and not on the ray 1 4 of the negative real axis using related properties of continued fractions we obtain the t m process considered by gray and clark and the process considered by w j thron and h waadeland it follows the possibility of choosing the best process according to the convergence behaviour of the sequences a n

on group theoretic codes for asymmetric channels we study single error correcting codes for the asymmetric channel with input and output alphabets being 0 1 a 1 from an abelian group g of order n with elements g0 0 g1 gn 1 constantin and rao 1979 inform contr 40 20 36 define vg b1 b2 bn 1 o 1 a 1 n 1 n 1i 1 bigi 0 g and show that vg correct single errors we give explicit expressions for the size and weight distribution of these codes we further give a short discussion of some constant weight codes obtained by a similar construction

applications of the heine and bauer muir transformations to rogers ramanujan type continued fractions abstract in this paper we show that various continued fractions for the quotient of general ramanujan functions g a q b q g a b may be derived from each other via bauer muir transformations the separate convergence of numerators and denominators play a key part in showing that the continued fractions and their bauer muir transformations converge to the same limit we also show that these continued fractions may be derived from either heine s continued fraction for a ratio of 1 2 functions or other similar continued fraction expansions of ratios of 1 2 functions further by employing essentially the same methods a new continued fraction for g a q b q g a b is derived finally we derive a number of new versions of some beautiful continued fraction expansions of ramanujan for certain combinations of infinite products with the following being an example a b q a b q a b q a b q a b 1 a b 1 a 2 1 b 2 q 1 a b q 2 a b q 2 b a q 2 q 1 a b q 4 1 a 2 q 2 1 b 2 q 2 q 3 1 a b q 6 a b q 4 b a q 4 q 3 1 a b q 8

adaptation of the mactaggart and jack complex multiplication algorithm for floating point operators with a suitable treatment of the exponents in the input operands a hardware implementation of the mactaggart and jack fixed point complex multiplication algorithm can also calculate a floating point product with no loss in accuracy from the greater dynamic range of the floating point inputs this floating point technique can be extended to any sum to two products operation such as encountered in matrix multiplication and vector cross products

new lower bounds for asymmetric and unidirectional codes new lower bounds on the sizes of asymmetric codes and unidirectional codes are presented various methods are used three of them of special interest the first is a partitioning method that is a modification of a method used to construct constant weight codes the second is a combining codes method that is used to obtain a new code from a few others the third method is shortening by weights that is applied on symmetric codes or on codes generated by the combining codes method tables for the sizes of codes of length n

a note on free flexural vibrations of a non uniform elliptical ring in its plane abstract an approximate solution for the title problem is obtained by using the rayleigh ritz method two different types of co ordinate functions are used sinusoids and polynomial expressions which contain an undetermined exponential parameter which allows for minimization of the natural frequency coefficients continuous and discontinuous variation of the ring thickness are considered the analytical predictions are compared with values obtained by means of the finite element method and good engineering agreement is shown to exist no claim of originality is made but it is hoped that present results will be of interest to designers

in plane vibrations of circular rings on a tensionless foundation abstract the problem of a thin elastic circular ring on a tensionless winkler foundation is considered it is assumed that the ring is subjected to time dependent in plane loads the analysis is based on the harmonic approximation for the deflection function of the ring the governing equations of the problem are derived by employing lagrange s equations the static and dynamic responses of the ring are obtained numerically and presented in figures comparatively for conventional and for tensionless winkler foundations

extended procedures for extrapolation to the limit in this paper new procedures for the extrapolation to the limit of slowly convergent sequences and functions are proposed they are based on the notions of error estimates and annihilation operators we obtain generalizations of the discrete and confluent e transformation which are the most general sequence and function transformations known so far it is shown that many transformations studied in the literature are included in our formalism particular cases of these procedures are discussed then several extensions of the e algorithm are given finally the procedure q is applied to our procedures to produce new procedures for extrapolation to the limit

truncation error bounds for modified continued fractions with applications to special functions much recent work has been done to investigate convergence of modified continued fractions mcf s following the proof by thron and waadeland 35 in 1980 that a limit periodic mcfk a n 1 x 1 with mathop lim limits n to infty a n a in mathbb c infty tfrac 1 4 andnth approximant g n s n x 1 frac a 1 1 frac a 2 1 cdots frac a n 1 1 frac a n 1 x 1 converges more rapidly to its limitf than the ordinary reference continued fractionk a n 1 withnth approximantf n s n 0 herex 1 denotes the smaller in modulus of the two fixed points oft w a 1 w the present paper gives truncation error bounds for bothf n andg n that exploit the limit periodic property lima n a certain a posteriori bounds given forg n are shown to be best possible relative to the given limited information available this is the first instance in which truncation error bounds for this problem have been shown to be best possible also included in this paper are results on speed of convergence a practical method for constructing the bounds and applications to a number of special functions the given numerical examples indicate that the error bounds are indeed sharp for the function arctanz we give graphical contour maps of the number of significant digits in the approximationsf n z g n z andp n z thenth partial sum of the maclaurin series forz in a key region of the complex plane these maps help us compare the various approximations with each other and add to our understanding of their convergence behavior

frequency analysis of a uniform ring perturbed by point masses and springs abstract perturbation expansions of solutions for a uniform thin linear elastic ring perturbed by point masses and radial massless springs are developed the perturbation locations divide the ring into uniform segments so a variational formulation is used to determine the boundary conditions that must be satisfied between adjoining segments the motion of each segment can be represented as a weighted sum of the eigenfunctions for the uniform thin ring so when the boundary conditions are enforced the resulting algebraic relations are expanded as a function of the perturbation parameter the perturbation mass normalized by the ring mass a series of algebraic problems are sequentially solved to yield perturbation expansions for the modal frequencies and eigenmodes single mass dual mass and mass spring case studies are considered the perturbation results show excellent agreement with finite element analysis of a thin ring for mass perturbations up to 15 of the nominal ring mass the results are also compared to rayleigh ritz analysis

upper bounds on codes correcting asymmetric errors corresp a survey is given of known upper bounds on codes correcting asymmetric errors the bounds are improved by introducing new ideas by solving a linear programming problem an upper bound is given that is easy to compute for all codelengths and all minimum asymmetric distances

greedy and heuristic algorithms for codes and colorings many of the fundamental coding problems can be represented as graph problems these problems are often intrinsically difficult and unsolved even if the code length is relatively small with the motivation to improve lower bounds on the sizes of constant weight codes and asymmetric codes we suggest a few greedy algorithms and other heuristic methods which result in new record breaking codes some of the heuristics used are based on tabu search and evolutionary algorithms tables of new codes are presented

new bounds and constructions for granular media coding improved lower and upper bounds on the size and the rate of grain correcting codes are presented the lower bound is gilbert varshamov like combined with a construction by gabrys et al and it improves on the previously best known lower bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval 0 0 0668 one of the two newly presented upper bounds improves on the best known upper bounds on the asymptotic rate of lceil tau n rceil grain correcting codes of length n on the interval tau in 0 1 8 and meets the lower bound of 1 2 for tau geq 1 8 moreover in a nonasymptotic regime both upper bounds improve on the previously best known results on the largest size of t grain correcting codes of length n for certain values of n and t constructions of 1 grain correcting codes based on a partitioning technique are presented for lengths up to 18 finally a lower bound of 1 2 log 2 n on the minimum redundancy of infty grain detecting codes of length n is presented

bounds and constructions for binary asymmetric error correcting codes corresp by use of known bounds on constant weight binary codes new uppper bounds are obtained on the cardinality of binary codes correcting asymmetric errors some constructions are exhibited that come close to these bounds for single error correcting codes some constructions are derived from the steiner system s 5 6 12 and for double error correcting codes some constructions are derived from the nordstrom robinson code

contraction properties of sequence transformations since convergence acceleration is sometimes difficult to achieve a new concept the contraction of a sequence transformation is introduced and studied after some definitions an introductory example is given then some general results follow and aitken s 2 process is examined in more details the theta procedure is studied and some conclusions and perspectives are evocated

some new binary codes correcting asymmetric unidirectional errors the authors give a tabulation of the numbers of codewords in new binary codes with the asymmetric unidirectional error correcting capabilities of 3 4 5 6 for lengths 14 15 23 the new codes have greater sizes than the known codes for 14

spectral enumerators for certain additive error correcting codes over integer alphabets the paper contains a study of certain block codes with integer coordinate symbols devised for the correction of some types of additive errors the codes are defined by a check equation over a finite abelian group thus they appear as an extension of the varshamov and constantin rao codes the main results of the paper are concerned with the error correcting capability including a decoding method for generalized varshamov codes and principally with enumeration problems a general formula for spectral enumerators is obtained and applied to the varshamov and constantin rao codes

new lower bounds for constant weight codes some new lower bounds are given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance 4 and constant weight w in a number of cases the results significantly improve on the best bounds previously known

outer bounds on the capacity of interference channels corresp new outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and gaussian interference channels the bound for discrete channels coincides with the capacity region in special cases the bound for gaussian channels improves previous knowledge when the interference is of medium strength

new upper bounds on the size of codes correcting asymmetric errors corresp new upper bounds on the size of codes correcting asymmetric errors are derived by sharpening some of the constraints in the integer programming problem of delsarte and piret it is shown that their code for length 9 and asymmetric distance 2 is optimal

stabilization for an ensemble of half spin systems feedback stabilization of an ensemble of non interacting half spins described by the bloch equations is considered this system may be seen as an interesting example for infinite dimensional systems with continuous spectra we propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin 1 2 or 1 2 the proof of the convergence is done locally around the equilibrium in the h 1 topology this local convergence is shown to be a weak asymptotic convergence for the h 1 topology and thus a strong convergence for the c 0 topology the proof relies on an adaptation of the lasalle invariance principle to infinite dimensional systems numerical simulations illustrate the efficiency of these feedback laws even for initial conditions far from the equilibrium

natural frequencies and modes of rings that deviate from perfect axisymmetry given the experimental or theoretical natural frequencies and modes of an axisymmetric ring an analytical method is presented that allows one to obtain the natural frequencies and modes when this ring is non axisymmetric due to a mass or stiffness non uniformity of the ring a ring is the simplest model of an axisymmetric structure and treatment of its non uniformities paves the way for treatment of more complicated structures such as tires for example the receptance method is employed to determine the natural frequencies and mode shapes of a circular ring which is deviating from axisymmetry due to a local mass of stiffness non uniformity the receptance of the ring is derived by utilizing the modal expansion method

a multigrid version of a simple finite element method for the stokes problem we consider a finite element method for the stokes problem on a rectangular domain based on piecewise bilinear velocities and piecewise constant pressures on a uniform rectangular grid it is shown that by a simple stabilization strategy the method can be implemented in a convergent multigrid procedure introduction one of the most natural ways of discretizing the stokes equations on a two dimensional rectangular domain is to apply the finite element techniques with continuous piecewise bilinear velocities and piecewise constant pressures on a rectangular grid this method is easily extended to more general quadrilateral meshes and it has proved to be quite effective in practice the convergence analysis of the method was first carried out in 10 on a rectangular domain in 12 the estimates of 10 are improved and extended to more general quadrilateral meshes so far the above method has been used mainly in connection with direct band solvers usually combined with penalty perturbation techniques to eliminate the pressure 9 in this paper we consider an iterative variant of the method based on multigrid techniques such an algorithm seems attractive especially since the un derlying finite difference equations are relatively simple multigrid methods for the stokes problem and for more general elliptic systems were considered previously by hackbusch 8 and verfurth 14 in 14 it is shown that a convergent multigrid algorithm for the stokes problem can be constructed by appropriately scaling the variables provided that the underlying finite element scheme satisfies the babu ka brezzi stability condition 2 5 in our case however the finite element method is not stable in this sense and we have not been able to show that the straightforward application of the algorithm proposed in 14 yields a convergent process therefore we suggest first modifying the finite element method in such a way that it becomes stable in the ordinary sense the usual way of stabilizing an unstable mixed method is to add more velocity or primary variables a classical example of this is the quadratic linear velocity pres sure element of crouzeix and raviart 6 where added bubble functions act as stabilizers in the velocity space increasing the dimension of the velocity space would be an alternative in our case however we propose another method which seems to yield a simpler algorithm it is based on adding an extra stabilizing term into the

constructions and bounds for systematic tec aued codes several methods of constructing systematic t error correcting all unidirectional error detecting codes are described these codes can be constructed by adding a tail to a linear t error correcting code but other constructions presented are more of an ad hoc nature these codes will often be found as suitably chosen subsets of nonsystematic tec aued codes further bounds on the word length of systematic tec aued codes are derived and extensive tables are given

a study on the mode pair of a slightly asymmetric circular ring with multiple deviations this paper theoretically investigates the effect of multiple local deviations on the property of mode pair of a circular ring the laplace transform method is applied to the asymmetric ring with multiple local deviations multiple heavy side step functions are used to model the local deviations by using distributed mass stiffness and thickness elements the effect of multiple deviations on the change of the frequency of the mode pair is investigated beat frequency and configuration of the mode pair are investigated according to the amount and the position of the deviation this study aims to explain the deviation effect on the beats of rings and bell type structures the proposed analytical method can be used to control the beat characteristics of bell type structures

on symmetric error correcting and all unidirectional error detecting codes the design of binary block codes that are capable of correcting up to t symmetric errors and detecting all unidirectional errors is discussed a class of systematic t symmetric error correcting all unidirectional error detecting t syec aued codes are proposed when t 0 the proposed codes become berger codes for t 1 the proposed codes are shown to be of asymptotically optimal order methods to construct nonsystematic t syec aued codes for t 2 and 3 are also presented

truncation error bounds for limit periodic continued fractionsk an 1 with liman 0 truncation error bounds are developed for continued fractionsk a n 1 where a n 1 4 for alln sufficiently large the bounds are particularly suited some are shown to be best for the limit periodic case when lima n 0 among the principal results is the following if a n n p for alln sufficiently large with constants 0 p 0 then f f m c d m 2 p m 2 for allm sufficiently large for some constantsc 0 d 0 heref denotes the limit assumed finite ofk a n 1 andf m denotes itsmth approximant applications are given for continued fraction expansions of ratios of kummer functions1 f 1 and of ratios of hypergeometric functions0 f 1 it is shown thatp 1 for1 f 1 andp 2 for0 f 1 wherep is the parameter determining the rate of convergence numerical examples indicate that the error bounds are indeed sharp

exact and approximate expressions for the probability of undetected errors of varshamov tenengol ts codes computation of the undetected error probability for error detecting codes over the z channel is an important issue explored only in part in previous literature in this paper varshamov tenengol ts vt codes are considered first an exact formula for the probability of undetected errors is given it can be explicitly computed for small code lengths up to approximately 25 next some lower bounds that can be explicitly computed up to almost twice this length are studied a comparison to the hamming codes is given it is further shown that heuristic arguments give a very good approximation that can easily be computed even for large lengths finally monte carlo methods are used to estimate performance for long code lengths

on the bauer muir transformation for continued fractions and its applications abstract we show that the bauer muir transformation is useful also for continued fractions with non positive elements some examples of applications of this transformation are studied

the in plane vibration of thin rings with in plane profile variations part ii application to nominally circular rings abstract geometric profile variations always exist in nominally circular rings due to limitations in the manufacturing processes such profile variations are known to lead to frequency splitting between pairs of modes which are degenerate in a perfect ring in this paper the effects of circumferential profile variations on the in plane vibration characteristics of such rings are studied using a numerical method the inner and outer ring surfaces are described in a very general way by fourier series and the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a number of example cases which include single and multiple harmonic variations in profile the relationship between the patterns of frequency splitting and the harmonic content of the ring profile is investigated and the most important causes of frequency splitting are identified

composite sequence transformations the aim of this work is to introduce the new concept of composite sequence transformations and to show by very simple examples and theorems that it can be useful in accelerating the convergence of sequences generalizations of classical transformations and results are obtained

bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6 upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance delta are derived for some values of n and delta a method is given in which a code of length n m and asymmetric distance at least t 1 is constructed by expurgating and puncturing a code of length n and hamming distance at least 2t 1 novel asymmetric error correcting codes are constructed by applying this method to some celebrated symmetric error correcting codes a table is presented on the size of optimal asymmetric error correcting codes of length less than 24 and asymmetric distance less than 6

lexicographic codes error correcting codes from game theory lexicographic codes or lexicodes are defined by various versions of the greedy algorithm the theory of these codes is closely related to the theory of certain impartial games which leads to a number of surprising properties for example lexicodes over an alphabet of size b 2 a are closed under addition while if b 2 2 a the lexicodes are closed under multiplication by scalars where addition and multiplication are in the nim sense explained in the text hamming codes and the binary golay codes are lexieodes remarkably simple constructions are given for the steiner systems s 5 6 12 and s 5 8 24 several record breaking constant weight codes are also constructed

successive modifications of limit periodic continued fractions it is well known that limit periodic continued fractions can be accelerated by modifications using converging factors in this paper the repeated use of modifications is studied in the case of a constant converging factor and in the case of aitken s d 2 process based on these modifications a method for controlling the error is proposed

remarks to a definition of convergence acceleration illustrated by means of continued fractions k a n 1 where a n 0 abstract let cn and c n be two sequences of complex numbers converging to the finite limit c we say that c n converges faster to c than cn if c n c c n c 0 convergence acceleration is based on this definition in this paper we draw attention to some of its deficiencies as an example we consider the case where cn is the sequence of approximants of a continued fraction k a n 1 where an 0

vibrations of non uniform rings studied by means of the differential quadrature method abstract the vibrational behavior of ring like structures is of interest in several technological situations from automotive and aircraft tires to electric motors and transformers this study deals with the solution of the governing sixth order differential equation by using the differential quadrature method the fundamental frequency of in plane inextensional vibration is thus determined and compared with the value predicted by the optimized rayleigh ritz method

in plane vibrations of circular rings of non uniform cross section with account taken of shear and rotatory inertia effects abstract the solution of the title problem is obtained by using the finite element method explicit expressions are derived for a generic element of the ring s circular central axis the methodology yields numerical results which are in excellent agreement with values available in the open literature frequency coefficients are presented for circular ring configurations of non uniform cross section which have significant technological importance and which have not been considered previously in the literature at least not when shear and rotatory inertia effects are taken into account

constructions for perfect mixed codes and other covering codes a construction for an infinite family of perfect mixed codes with covering radius 2 is presented these are the first known nontrivial perfect mixed codes with covering radius greater than 1 based on mixed codes constructions for binary covering codes that lead to a considerable improvement of upper bounds on the sizes of covering codes are presented these codes and some other codes can be obtained by the blockwise direct sum construction two infinite families of codes are of special interest they are quasi perfect nonlinear union of their disjoint translates covers the space and their density as covering codes is remarkably low

unidirectional covering codes a code c spl sube z sup n sub 2 where z sub 2 0 1 has unidirectional covering radius r if r is the smallest integer so that any word in z sup n sub 2 can be obtained from at least one codeword c spl isin c by replacing either 1s by 0s in at most r coordinates or 0s by 1s in at most r coordinates the minimum cardinality of such a code is denoted by e n r upper bounds on this function are here obtained by constructing codes using tabu search lower bounds on the other hand are mainly obtained by integer programming and exhaustive search best known bounds on e n r for n spl les 13 and r spl les 6 are tabulated

on the acceleration of limit periodic continued fractions a continued fraction c f k a n 1 is called limit periodic if mathop lim limits n to infty a n a fora anda 1 4 a 0 thron waadeland 1980 examined a modification of a limit periodic c f for accelerating the convergence this acceleration remains modest if thea n converge only logarithmically thus it is proposed to apply an euler summability method to the series equivalent to the c f properties of the equivalent function are derived these properties are used for choosing appropriate parameters for the summability method such that a considerable acceleration can be expected even if thea n converge logarithmically

vibration analysis of a nearly axisymmetric shell structure using a new finite ring element abstract a new conical ring element to be used in connection with the finite element method fem is developed which considers the effects of slight local deviations from an axisymmetric ring to develop the proposed finite element the displacements of a point in the ring element are assumed by a pair of the natural modes of a ring with local deviation symmetric and asymmetric modes by using the presented finite elements a fem program is also developed to analyze free vibrations of a nearly axisymmetric shell structure the developed program is applied to a vibration analysis of a korean bell as an example which shows that the program is very efficient and saves much computation time for shell structures slightly deviating from axisymmetry compared to commercial fem codes

calculation of poles of meromorphic functions with q d r s and e algorithms acceleration of these processes we study sections 1 and 2 the speed of convergence of the q d algorithm to poles of a meromorphic function in order to accelerate it in section 3 and 4 we show that the quotient of two successive vertical terms of two well known algorithms r s and e approaches also these poles at last a theorem of acceleration is given

the threshold probability of a code we define and estimate the threshold probability spl theta of a linear code using a theorem of margulis 1974 originally conceived for the study of the probability of disconnecting a graph we then apply this concept to the study of the erasure and z channels for which we propose linear coding schemes that admit simple decoding we show that spl theta is particularly relevant to the erasure channel since linear codes achieve a vanishing error probability as long as p spl lesspl theta where p is the probability of erasure in effect spl theta can be thought of as a capacity notion designed for codes rather than for channels binomial codes haven the highest possible spl theta and achieve capacity as for the z channel a subcapacity is derived with respect to the linear coding scheme for a transition probability in the range log 3 2 1 we show how to achieve this subcapacity as a by product we obtain improved constructions and existential results for intersecting codes linear sperner families which are used in our coding schemes

convergence acceleration of limit periodic continued fractions under asymptotic side conditions we present a method of convergence acceleration for limitk periodic continued fractionsk an 1 ork 1 bn satisfying certain asymptotic side conditions the method represents an improvement of the fixed point modification considered by thron and waadeland 8 under these conditions the regularc fraction expansions of hypergeometric functions2f1 a 1 c z and2f1 a b c z 2f1 a b 1 c 1 z are examples of continued fractions satisfying these conditions

a note on the relation between two convergence acceleration methods for ordinary continued fractions in this note we relate two methods of convergence acceleration for ordinary continued fractions the first one is due to lorentzen and waadeland jacobsen and waadeland 1980 1998 the second one to waadeland 1986 1987 1987 1987 1988

new constructions of codes for asymmetric channels via concatenation we present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets based on methods of generalized code concatenation for the binary asymmetric channel our methods construct nonlinear single error correcting codes from ternary outer codes we show that some of the varshamov tenengol ts constantin rao codes a class of binary nonlinear codes for this channel have a nice structure when viewed as ternary codes in many cases our ternary construction yields even better codes for the nonbinary asymmetric channel our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors

theory of unidirectional error correcting detecting codes in this paper we present some basic theory on unidirectional error correcting detecting codes we define symmetric asymmetric and unidirectional error classes and proceed to derive the necessary and sufficient conditions for a binary code to be unidirectional error correcting detecting

a single asymmetric error correcting code with 2 sup 13 codewords of dimension 17 a new single asymmetric error correcting code is proposed this code is constructed using a product of two codes of smaller dimensions the proposed code is of dimension 17 and of size 8192 i e with 2 sup 13 codewords the best known code of dimension 17 has size 7968 and capable of handling 12 information bits only the only other three known cases of single asymmetric codes accommodating one more extra information bit than the symmetric case are for code dimensions 2 4 and 16

on a khovanskii transformation for continued fractions abstract some aspects of a transformation for continued fractions due to khovanskii are studied it is shown that the transformation does not in general establish an identity but has many interesting properties it permits to transform some difficult continued fractions into suitable ones its even part is identical to the even part of s n 1 2 modification it may also give acceleration for some slow continued fractions

the in plane vibration of thin rings with in plane profile variations part i general background and theoretical formulation abstract this paper presents a methodology for the analysis of the free in plane vibration of thin rings with profile variations in the circumferential direction the methodology is suitable for any thin ring which is bounded by closed curves which are single valued functions of circumferential position the inner and outer profiles are expressed as fourier series thus allowing any profile to be approximated with any degree of accuracy an iterative numerical procedure for determining the true middle surface and the corresponding thickness at each cross section around the circumference is established a reduced plane stress form of novozhilov s thin shell theory is used to model the deformation mechanics of the ring the eigenvalue problem is then formulated using the rayleigh ritz method in conjunction with a harmonic series description of the displacements general expressions are presented for the corresponding mass and stiffness matrices a companion paper presents a comprehensive set of results which illustrates application of the theory

new lower bounds for binary codes of asymmetric distance two lower bounds for asymmetric single error correcting codes are derived the codes are constructed by puncturing constant weight codes and by using a random coding argument

aitken sequences and generalized fibonacci numbers consider the sequence t generated by t i avn bv l l n 5i 2 where vi 1 t 2 a with a and b real of which the fibonacci sequence is a special case it is shown that if aitken acceleration is used on the sequence x defined by a v 1 v the resulting sequence is a subsequence of jc second if newton s method and the secant method are used with suitable starting values to solve the equation x2 ax b 0 then the sequences obtained from both of those methods are also subsequences of the original sequence

new single asymmetric error correcting codes new single asymmetric error correcting codes are proposed these codes are better than existing codes when the code length n is greater than 10 except for n 12 and n 15 in many cases one can construct a code c containing at least 2 sup n n codewords it is known that a code with c spl ges 2 sup n n 1 can be easily obtained it should be noted that the proposed codes for n 12 and n 15 are also the best known codes that can be explicitly constructed since the best of the existing codes for these values of n are based on combinatorial arguments useful partitions of binary vectors are also presented

improving a method for computing non dominant solutions of certain second order recurrence relations of poincare type in this paper we present a method of convergence acceleration for the calculation of non dominant solutions of second order linear recurrence relations for which the coefficients satisfy certain asymptotic conditions it represents an improvement of the method recently proposed by jacobsen and waadeland 3 4 for limit periodic continued fractions for continued fractions the method corresponds to a repeated application of the bauer muir transformation some examples and a generalization to non homogeneous recurrence relations are given

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

convergence acceleration for continued fractions _ 1 a known method for convergence acceleration of limit periodic con tinued fractions k an a a is to replace the approximants 5 0 by modified approximants sn f where k a the present paper extends this idea to a larger class of converging continued fractions the modified approximants will then be 5 n where k a n is a converging continued fraction whose tails are all known and where a a n 0 as a measure for the improvement obtained by this method upper bounds for the ratio of the two truncation errors are found

a new method for in plane vibration analysis of circular rings with widely distributed deviation abstract a new analytical method was developed to predict the in plane mode shapes and the natural frequencies of a ring with widely distributed deviation the laplace transform was used to find the exact solution of eigenvalue problem without assuming any trial functions and finite elements the widely distributed deviation was effectively formulated in the theory using gauss legendre quadrature the validity of the proposed method was examined through finite element analysis and modal test the effects of partial change of the density the stiffness and the thickness on the natural frequencies of the ring were investigated

repeated modifications of limitk periodic continued fractions the advantages of using modified approximants for continued fractions can be enhanced by repeating the modification process ifk a n b n is limitk periodic a natural choice for the modifying factors is ak periodic sequence of right or wrong tails of the correspondingk periodic continued fraction if it exists if the modified approximants thus obtained are ordinary approximants of a new limitk periodic continued fraction we repeat the process if possible some examples where this process is applied to obtain a convergence acceleration are also given