near optimal limited search detection on isi cdma channels and decoding of long convolutional codes we derive an upper bound on the bit error probability bep in limited search detection over a finite interference channel a unified channel model is presented this includes finite length intersymbol interference channels and multiuser cdma channels as two special cases we show that the bep of the m algorithm ma is bounded from above by the sum of three terms an upper bound on the error probability of the viterbi 1967 algorithm va detection given by forney jr 1972 and upper bounds on the error probabilities of two types of erroneous decision caused by the correct path loss event we prove that error propagation in terms of the mean recovery step number is finite for all finite interference channels the convergence and asymptotic behavior of the upper bounds are studied the results show that if a channel satisfies certain mild conditions all series in the bounds are convergent one of the key results is that for any finite interference channel satisfying certain mild conditions the asymptotic bep of the ma is bounded by the same upper and lower bounds which have the same asymptotical behavior as those for the va if the correct path loss probability is smaller than that of the va furthermore we extend the above results to near optimally decode long convolutional codes in a short packet format about 200 300 bits we present a nonsorting combined m t algorithm and showed that the m t algorithm with m 2 sup d free sup n and t d sub free e sub b n can near optimally decode the code we also propose a hierarchical decoding algorithm hda to further cut down the average decoding complexity numerical results show that the bounds are reasonably tight the hda can achieve a performance within about 0 8 db of the sphere packing lower bound for a packet error rate of 10 sup 4 and a packet length below 200 bits which is the best reported decoding performance so far for block sizes from 100 to 200 bits

symmetry based solution of a model for a combination of a risky investment and a riskless investment abstract benth and karlsen f e benth k h karlsen a note on merton s portfolio selection problem for the schwartz mean reversion model stoch anal appl 23 2005 687 704 treated a problem of the optimisation of the selection of a portfolio based upon the schwartz mean reversion model the resulting hamilton jacobi bellman equation in 1 2 dimensions is quite nonlinear the solution obtained by benth and karlsen was very ingenious we provide a solution of the problem based on the application of the lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions

a fast algorithm for computing distance spectrum of convolutional codes a fast algorithm for searching a tree fast is presented for computing the distance spectrum of convolutional codes the distance profile of a code is used to limit substantially the error patterns that have to be searched the algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event for testing systematic codes a faster version of the algorithm is given fast is much faster than the standard bidirectional search on a microvax d sub infinity 27 was verified for a rate r 1 2 memory m 25 code in 37 s of cpu time extensive tables of rate r 1 2 encoders are given several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory a conjecture than an r 1 2 systematic convolutional code of memory 2m will perform as well as a nonsystematic convolutional code of memory m is given strong support

tailbiting codes bounds and search results tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied the notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower bounded the asymptotic behavior of the derived bound is investigated furthermore for regular tailbiting codes the product state complexity is lower bounded tables of new tailbiting trellis representations of linear block codes of rates 1 2 1 3 and 1 4 are presented almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time varying trellises which are optimal five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters four of them are also superior to any previously known nonlinear code with the same parameters also more than 40 other quasi cyclic codes have been found that improve the parameter set of previously known quasi cyclic codes

the ladder problem painleve integrability and explicit solution we consider the n dimensional ladder system that is the homogeneous quadratic system of first order differential equations of the form where aij i 1 j i j 1 n introduced by imai and hirata 2002 preprint nlin si 0212007 v1 3 the ladder system is found to be integrable for all n in terms of the painleve analysis and its solution is explicitly given

the algebraic structure of generalized ermakov systems in three dimensions the characteristic algebra of generalized ermakov systems is sl 2 r the structure of these systems in three dimensions is obtained a subset in the form of an equation of motion with the additional requirement of so 3 symmetry is studied it includes the classical equation of the magnetic monopole the existence of three vectors of poincare type is established consideration is given to weak generalized ermakov systems in which the symmetry breaking occurs in the radial equation

a distance spectrum interpretation of turbo codes the performance of turbo codes is addressed by examining the code s distance spectrum the error floor that occurs at moderate signal to noise ratios is shown to be a consequence of the relatively low free distance of the code it is also shown that the error floor can be lowered by increasing the size of the interleaver without changing the free distance of the code alternatively the free distance of the code may be increased by using primitive feedback polynomials the excellent performance of turbo codes at low signal to noise ratios is explained in terms of the distance spectrum the interleaver in the turbo encoder is shown to reduce the number of low weight codewords through a process called spectral thinning this thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signal to noise ratios

symmetry and singularity properties of second order ordinary differential equations of lie s type iii abstract we extend the work of abraham shrauner b abraham shrauner hidden symmetries and linearization of the modified painleve ince equation j math phys 34 1993 4809 4816 on the linearization of the modified painleve ince equation to a wider class of nonlinear second order ordinary differential equations invariant under the symmetries of time translation and self similarity in the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations

hidden and contact symmetries of ordinary differential equations the lie algebra for the maximal contact symmetries of third order ordinary differential equations odes is examined for type i and ii hidden symmetries where the analysis of hidden symmetries for point symmetries is extended to contact symmetries ones invariant under the group associated with the ten dimensional maximal lie algebra may produce type i hidden symmetries for two parameter subgroups and type ii hidden symmetries for certain solvable non abelian three parameter subgroups in the third order odes when they are reduced in order a new class of type ii hidden symmetries is recognized in which contact symmetries transform to point symmetries in some reduction paths two examples of odes invariant under subgroups of the ten parameter group under which y 0 is invariant demonstrate the new class of type ii hidden symmetries

topological equivalence of flows on homogeneous spaces and divergence of one parameter subgroups of lie groups soient et des treillis et et des sous groupes a un parametre des groupes de lie connexes g et g si une des conditions a b ou c est vraie alors le theoreme a etablit que si les flots induits sur les espaces homogenes g et g sont topologiquement equivalents alors ils sont topologiquement equivalents par une application affine

lie subalgebras reduction of order and group invariant solutions one of the great utilities of lie symmetries of differential equations is in their use to reduce the order of ordinary differential equations and partial differential equations to ordinary differential equations this process is guided by the lie algebra of the symmetries admitted by the equation under study it is important in these reductions to use appropriate symmetries this will ensure that a sufficient number remain after the initial reduction to allow subsequent reductions by considering two and three dimensional subalgebras of the lie algebra of the symmetries of differential equations we indicate the fate of these symmetries under various reductions in doing so it is clear as to which symmetries need be prioritized in reduction

partial symmetry of initial value problems abstract it is generally believed that the symmetry of initial value problems ivp must leave both the partial differential equations pdes and initial conditions invariant in this paper we propose partial symmetry of ivp which needs less restrictive conditions on the pdes and initial conditions and only leaves the ivp invariant on some non empty subset of the whole solution set of the governing pdes thus some symmetries which either only leave the pdes invariant or only leave initial conditions invariant are partial symmetries of ivp then considering from two different starting points we define two types of partial symmetry and give the corresponding algorithms where one starts with the pdes and the other is from the initial conditions applications to boussinesq equation and a class of nonlinear heat equation are performed

symmetry analysis of a model of stochastic volatility with time dependent parameters we provide the solutions for the heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time in the former case the solution follows immediately from the determination of the lie point symmetries of the governing 1 1 evolution partial differential equation this is not the situation in the latter case but we are able to infer the essential structure of the required nonlocal symmetry from that of the autonomous problem and hence can present the solution to the nonautonomous problem as in the case of the standard black scholes problem the presence of time dependent parameters is not a hindrance to the demonstration of a solution

wavefunctions for the time dependent linear oscillator and lie point symmetries we investigate the solution of the quantal time dependent linear oscillator from the viewpoint of the lie point symmetries of its time dependent schrodinger equation four of the five nongeneric symmetries can be used for the construction of wavefunctions two as creation symmetries and two as annihilation symmetries the fifth nongeneric symmetry provides an eigenvalue for the lie bracket which maps a solution symmetry to itself the general treatment indicates that care must be taken with the selection of solutions of the classical equation for the time dependent linear oscillator and its third order self adjoint counterpart to obtain results which are consistent with the standard results for the autonomous harmonic oscillator

equivalence classes of second order ordinary differential equations with only a three dimensional lie algebra of point symmetries and linearisation there are seven equivalence classes of second order ordinary differential equations possessing only three lie point symmetries and hence not linearisible by means of a point transformation we examine the representatives of these classes for linearisibility by means of other types of transformation in particular we compare the potential for linearisibility and the possession of the painleve property the complete symmetry group is realised in the standard algebra for each of the equivalence classes

bit interleaved coded differential space time modulation bit interleaved coded differential space time modulation for transmission over spatially correlated ricean flat fading channels is discussed for improved noncoherent detection without channel state information at the receiver iterative decoding employing hard decision feedback and prediction based metric computation is applied the performance is assessed based on the associated cutoff rate analytical expressions for the bit error rate and the outage probability respectively and simulations it is shown that the proposed scheme offers high power efficiency exploiting both space and time diversity while the computational complexity is kept at a relatively low level

complete symmetry group and nonlocal symmetries for some two dimensional evolution equations abstract the complete symmetry group of an 1 1 evolution equation of maximal symmetry has been demonstrated to be represented by the six dimensional lie algebra of point symmetries sl 2 r s w where w is the three dimensional heisenberg weyl algebra we construct a complete symmetry group of a 1 2 evolution equation u t f u u x y for some functions f using the point symmetries admitted by the equation the 1 2 equation is not completely specifiable by point symmetries alone for some specific functions f we make use of ansatze already reported by myeni and leach s m myeni p g l leach nonlocal symmetries and complete symmetry groups of evolution equations j nonlinear math phys 13 2006 377 392 which provide a route to the determination of the required generic nonlocal symmetries necessary to supplement the point symmetries for the complete specification of these 1 2 evolution equations further we find that taking some suitable linear combination of lie point symmetries helps to optimise the procedure of specifying the equation a general result concerning the number of symmetries required to form a complete symmetry group of evolution is presented in the conclusion

complete symmetry groups of ordinary differential equations and their integrals some basic considerations abstract the concept of the complete symmetry group of a differential equation introduced by j krause 1994 j math phys 35 5734 5748 is extended to integrals of such equations this paper is devoted to some aspects characterising complete symmetry groups the algebras of the symmetries of both differential equations and integrals are studied in the context of equations for which the elements are represented by point or contact symmetries so that there is no ambiguity about the group both algebras and groups are found to be nonunique

the complete symmetry group of the generalised hyperladder problem abstract we further consider the n dimensional ladder system that is the homogeneous quadratic system of first order differential equations of the form x i x i j 1 n a ij x j i 1 n where aij i 1 j i j 1 n introduced by imai and hirata nlin si 0212007 we establish the most general system of first order ordinary differential equations invariant under the algebra which characterises the ladder system of imai and hirata and the algebra of minimal dimension required to specify completely this most general system we provide the complete symmetry group of the generalised hyperladder system and discuss its integrability

algebraic hulls and smooth orbit equivalence let mi ui i 1 2 be two manifolds with quasi invariant measures and let hi c diff mi be connected lie groups if there is a measure class preserving diffeomorphism 0 m1 m2 which is a bijection of hl orbits and h2 orbits then we say that the actions are smoothly orbit equivalent if the hi actions determine foliations g on the manifolds mis then the map 0 is just a diffeomorphism between the foliations these phenomena and the corresponding phenomena arising in situations in which the mi ai are just borel or topological hi spaces and the map 0 is a measure class preserving borel isomorphism or homeomorphism have been studied using a variety of techniques independently by several authors b cfw d1 d2 k pnz w1 w2 z2 z4 most of the results obtained require some strengthening of the hypotheses such as finiteness and invariance of the measures and amenability or semisimplicity in higher rank of the groups acting one of the results that we want to describe in this paper fits in this geometric setting and provides an obstruction in terms of a geometric invariant of the actions to the foliations being diffeomorphic recall that if h acts ergodically and by diffeomorphisms on the n dimensional manifold m the algebraic hull of the h action is the unique up to conjugacy smallest algebraic subgroup l c gl n r such that there exists a measurable h invariant reduction to l of the frame bundle on m on which h acts by automorphisms for an analytic definition see 2 and for the general context see z5 9 2 then the normal algebraic hull of the h action on m will be the projection of l in the direction normal to the orbits

on the complete symmetry group of the classical kepler system a rather strong concept of symmetry is introduced in classical mechanics in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey accordingly a complete symmetry group realization in mechanics must be endowed with the following two features 1 the group acts freely and transitively on the manifold of all allowed motions of the system 2 the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group this program is applied successfully to the classical kepler problem since the complete symmetry group for this particular system is here obtained the importance of this result for the quantum kinematic theory of the kepler system is emphasized

lie theory applications to problems in mathematical finance and economics this paper is devoted to show and explain some applications of lie theory to solve some problems in economics and mathematical finance so we put forward and discuss mathematical aspects and approaches for several economic problems which have been previously considered in the literature besides we also show our advances on this topic mentioning some open problems for future research

on trellis codes with a delay processor and a signal mapper it is already known that a trellis code t which is constructed by using the encoder of a convolutional code c with short constraint length followed by a delay processor and a signal mapper is equivalent to a trellis code with large constraint length in this paper we derive a new lower bound on the free distance of t which in some cases is better than the previously derived bound moreover instead of the decoding used in earlier publications we apply iterative decoding on both tailbiting and zero tail representations of t to take advantage of the new lower bound and in the meantime to decrease the associated error coefficient caused by the decoding used in earlier publications comparisons among various designs of such a trellis code and some well known coding methods are also provided

maximal subalgebra associated with a first integral of a system possessing sl 3 r algebra conventionally the symmetries of a dynamical system are used to determine the first integrals associated with the system in this paper the reverse procedure is adopted for one dimensional systems possessing sl 3 r symmetry the equivalence of such systems enables the free particle equation to be used as a vehicle it is observed that for three particular first integrals each gives rise to a triplet of generators having isomorphic algebras it is then shown how the knowledge of a first integral and its associated triplet enables one to obtain the remaining integrals and triplets

the ermanno bernoulli constants and representations of the complete symmetry group of the kepler problem the expression of the components of the equation of motion of the classical kepler problem in terms of the natural variables associated with the ermanno bernoulli constants leads naturally to the same equations as are obtained by the technique of reduction of order developed by nucci j math phys 37 1772 1996 reported by nucci and leach j math phys 42 746 2001 three representations of the complete symmetry group of the kepler problem are obtained from the three standard representations of the complete symmetry group of the simple harmonic oscillator the algebra of the complete symmetry group of the two dimensional kepler problem is identified to be a1 a3 3 the applicability of the results to other classes of problem such as the kepler problem with drag which possess a conserved vector of laplace runge lenz type is indicated the three dimensional kepler problem is shown to be completely specified by six symmetries rather than the eight previously reported by krause j math phys

ermakov systems velocity dependent potentials and nonlinear superposition we derive new ermakov systems with velocity dependent potentials the extended ermakov system presented contains all known one dimensional cases and many new systems these ermakov systems lead to a nonlinear superposition law for the solutions

exponential nonlocal symmetries and nonnormal reduction of order the conventional approach to double reduction of the order of an ordinary differential equation using lie symmetries is via the normal subgroups of point symmetries we show that provided that one is prepared to use nonlocal symmetries initial reduction by the nonnormal subgroup does not prevent the double reduction we further illustrate our results with the general third order equations invariant under the nonsolvable algebras sl 2 r of which the chazy equation is a noted example and so 3

a network flow approach to convolutional codes presents an alternative way of looking at convolutional codes as a network of flows from this association previous known classes of nonsystematic convolutional codes are reproduced the authors also present a decomposition of the problem of finding good convolutional codes into well known and structured problems such as the maximum flow problem the knapsack problem and the modular representation of block codes a spanning tree search algorithm is also proposed for finding good codes the authors consider the class of nonsystematic convolutional codes for which the encoders satisfy an equivalent property related to the feasibility of flow finally extensive tables show the new and the previous known codes

estimations of the transfer functions of noncatastrophic convolutional encoders a computational method which allows us to upper bound the solution of a wide class of systems of linear recurrent equations is proposed this method is used to estimate the transfer functions of noncatastrophic convolutional encoders

symmetry and singularity properties of the generalised kummer schwarz and related equations abstract we examine the generalised kummer schwarz equation and some of its generalisations from the viewpoints of symmetry and singularity analyses we determine the complete symmetry group of the general equation and show that different forms of the fourth order representative illustrate the three possible classes of laurent series to be expected in the course of the singularity analysis

space time code design for cpfsk modulation over frequency nonselective fading channels we derive a novel space time code stc design criterion for continuous phase frequency shift keying cpfsk over frequency nonselective fading channels our derivation is based on a specific matrix that is related to the input symbols of the cpfsk modulators with this code design criterion we propose a simple interleaved space time encoding scheme for cpfsk modulation over frequency nonselective correlated fading channels to exploit potential temporal and spatial diversity advantages such an encoding scheme consists of a ring convolutional encoder and a spatial encoder between which a convolutional interleaver is placed a decoding algorithm that generates symbol metrics for the viterbi decoder of convolutional codes from the spatial modulation trellis is examined simulation results confirm that the advantages of the combination of the interleaved convolutional encoding for temporal diversity and the spatial encoding for spatial diversity are promising for various system parameters

topological equivalence of foliations of homogeneous spaces for i 1 2 let fi be a lattice in a connected lie group gi and let xi be a connected lie subgroup of gi the double cosets rigxi provide a foliation jt of the homogeneous space fi gi assume that xi and x2 are unimodular and that jr has a dense leaf if gi and g2 are semisimple groups to which the mostow rigidity theorem applies or are simply connected nilpotent groups or are certain more general solvable groups we use an idea of d benardete to show that any topological equivalence of jr and 7 must be the composition of two very elementary maps an affine map and a map that takes each leaf to itself

symmetry and the chazy equation there are three different actions of the unimodular lie group sl 2 c on a two dimensional space in every case we show how an ordinary differential equation admitting sl 2 as a symmetry group can be reduced in order by three and the solution recovered from that of the reduced equation via a pair of quadratures and the solution to a linear second order equation a particular example is the chazy equation whose general solution can be expressed as a ratio of two solutions to a hypergeometric equation the reduction method leads to an alternative formula in terms of solutions to the lame equation resulting in a surprising transformation between the lame and hypergeometric equations finally we discuss the painleve analysis of the singularities of solutions to the chazy equation

the complete kepler group can be derived by lie group analysis it is shown that the complete symmetry group for the kepler problem as introduced by krause can be derived by lie group analysis the same result is true for any autonomous system

a beast for prowling in trees when searching for convolutional codes and tailbiting codes of high complexity it is of vital importance to use fast algorithms for computing their weight spectra which corresponds to finding low weight paths in their code trellises this can be efficiently done by a combined search in both forward and backward code trees a bidirectional efficient algorithm for searching such code trees beast is presented for large encoder memories it is shown that beast is significantly more efficient than comparable algorithms beast made it possible to find new convolutional and tailbiting codes that have larger free minimum distances than the previously best known codes with the same parameters tables of such codes are presented

on n n 1 convolutional codes with low trellis complexity we show that the state complexity profile of a convolutional code c is the same as that of the reciprocal of the dual code of c in case that minimal encoders for both codes are used then we propose an optimum permutation for any given n n 1 binary convolutional code that will yield an equivalent code with the lowest state complexity with this permutation we are able to find many n n 1 binary convolutional codes which are better than punctured convolutional codes of the same code rate and memory size by either lower decoding complexity or better weight spectra

initial value problems for evolutionary partial differential equations and higher order conditional symmetries we suggest a new approach to the problem of dimensional reduction of initial boundary value problems for evolution equations in one spatial variable the approach is based on higher order generalized conditional symmetries of the equations involved it is shown that reducibility of an initial value problem for an evolution equation to a cauchy problem for a system of ordinary differential equations can be fully characterized in terms of conditional symmetries which leave invariant the equation in question we also give some examples of the solution of initial value problems for second and third order nonlinear differential equations by reduction by their conditional symmetries we give a systematic classification of general second order partial differential equations admitting second order conditional symmetries based on lie s classification of invariant second order ordinary differential equations this yields five classes of principally new initial value problems for nonlinear evolution equations which admit no lie symmetries and are reducible via second order conditional symmetries

the determination of nonlocal symmetries by the technique of reduction of order autonomous systems of ordinary differential equations can be rewritten as systems of first order ordinary differential equations and one of the dependent variables chosen as a new independent variable some of the variables are eliminated to give a mixed system of first and second order equations for which the determination of point symmetries can be automated without having to make an ansatz on the detailed structure of the symmetry because the coefficient function for the original independent variable appears only as its derivative in the reduced system symmetries which are nonlocal in this variable become local symmetries of the reduced system and can be computed algorithmically

nonlocal symmetries and integrable ordinary differential equations x 3xx x3 0 and its generalizations the equation x 3xx x3 0 is well known in many areas of mathematics and physics it possesses the algebra sl 3 r of lie point symmetries hence is equivalent to the equation for a free particle and both left and right painleve series we investigate two higher dimensional analogs in terms of their symmetry and singularity structures we find a drastic reduction in symmetry and a loss of some of the singularity properties from the nonlocal symmetries we are able to determine the complete symmetry group as being represented by a five dimensional abelian algebra

air polynomials lie point symmetries and a hyperbolic equation the solution of the problem of one dimensional unsteady isentropic gas flow with the use of riemann s invariants gives rise to a linear hyperbolic partial differential equation with the ratio of specific heats as an essential parameter the partial differential equation has 3 1 lie point symmetries the classical solutions are recovered with the use of the nongeneric symmetries to construct similarity solutions further solutions both polynomial and other are constructed using the invariants of the lie point symmetries as seed solutions and the property of mapping solutions into solutions these solutions are analogous to the well known heat polynomials

lie algebraic approach for pricing moving barrier options with time dependent parameters in this paper we apply the lie algebraic technique for the valuation of moving barrier options with time dependent parameters the value of the underlying asset is assumed to follow the constant elasticity of variance cev process by exploiting the dynamical symmetry of the pricing partial differential equations the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly and thus provides an efficient way for computing the prices of the moving barrier options the method is also able to provide tight upper and lower bounds for the exact prices of cev barrier options with fixed barriers in view of the cev model being empirically considered to be a better candidate in equity option pricing than the traditional black scholes model our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term structures of interest rates volatility and dividend into the cev option valuation model

some extended results on the search for good convolutional codes we provide useful results on two classes of convolutional codes binary codes and nonbinary codes the best codes or the best known codes for these two classes of convolutional codes are found by computer search some of them are better than those found in the past we specify these codes by their transfer function matrices distance spectra and information weight spectra furthermore we derive an upper bound on the free distances of binary to m ary codes and q ary to m ary codes numerical values of this bound closely fit the computer searched values

symmetry lie algebras of nth order ordinary differential equations abstract we show that an nth n 3 order linear ordinary differential equation has exactly one of n 1 n 2 or n 4 the maximum point symmetries the lie algebras corresponding to the respective numbers of point symmetries are obtained then it is shown that a necessary and sufficient conditon for an nth n 3 order equation to be linearizable via a point transformation is that it must admit the n dimensional abelian algebra na1 a1 a1 a1 we discuss in detail the symmetry realizations of n 1 a1 s a1 finally we prove that an nth n 3 order equation q n h t q qn 1 cannot admit exactly an n 3 dimensional algebra of point symmetries which is a subalgebra of na1 gl 2 r

evaluating the performance of convolutional codes over block fading channels this correspondence considers union upper bound techniques for error control codes with limited interleaving over block fading rician channels a modified bounding technique is presented that relies on limiting the conditional union bound before averaging over the fading process this technique although analytically not very attractive provides tight and hence useful numerical results

new rate 1 2 1 3 and 1 4 binary convolutional encoders with an optimum distance profile tabulations of binary systematic and nonsystematic polynomial convolutional encoders with an optimum distance profile for rate 1 2 1 3 and 1 4 are given the reported encoders are found by computer searches that optimize over the weight spectra the free distances for rate 1 3 and 1 4 are compared with heller s 1968 and griesmer s 1960 upper bounds

characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry abstract we undertake a study of the first integrals of linear n th order scalar ordinary differential equations with maximal symmetry we establish patterns for the first integrals associated with these equations it is shown that second and third order equations are the pathological cases in the study of higher order differential equations the equivalence of contact symmetries for third order equations to non cartan symmetries of second order equations is highlighted

euler bernoulli beams from a symmetry standpoint characterization of equivalent equations abstract we completely solve the equivalence problem for euler bernoulli equation using lie symmetry analysis we show that the quotient of the symmetry lie algebra of the bernoulli equation by the infinite dimensional lie algebra spanned by solution symmetries is a representation of one of the following lie algebras 2 a 1 a 1 a 2 3 a 1 or a 3 3 a 1 each quotient symmetry lie algebra determines an equivalence class of euler bernoulli equations save for the generic case corresponding to arbitrary lineal mass density and flexural rigidity we characterize the elements of each class by giving a determined set of differential equations satisfied by physical parameters lineal mass density and flexural rigidity for each class we provide a simple representative and we explicitly construct transformations that maps a class member to its representative the maximally symmetric class described by the four dimensional quotient symmetry lie algebra a 3 3 a 1 corresponds to euler bernoulli equations homeomorphic to the uniform one constant lineal mass density and flexural rigidity we rigorously derive some non trivial and non uniform euler bernoulli equations reducible to the uniform unit beam our models extend and emphasize the symmetry flavor of gottlieb s iso spectral beams h p w gottlieb isospectral euler bernoulli beam with continuous density and rigidity functions proc r soc lond ser a math phys eng sci 413 1987 235 250

the algebraic structure of the first integrals of third order linear equations we use the lie theory of extended groups to analyse the first integrals of scalar third order linear ordinary differential equations the analysis reveals three natural classes for which the equation has four five or seven symmetries we show that each class has first integrals with a specific number of symmetries illustrative examples of each class are given comparison is made with the integrals of nonlinear equations

efficient computation and optimization of the free distance of variable length finite state joint source channel codes this paper considers the optimization of a class of joint source channel codes described by finite state encoders fses generating variable length codes it focuses on fses associated to joint source channel integer arithmetic codes which are uniquely decodable codes by design an efficient method for computing the free distance of such codes using dijkstra s algorithm is proposed to facilitate the search for codes with good distance properties fses are organized within a tree structure which allows the use of efficient branch and prune techniques avoiding a search of the whole tree

discrete point symmetries of ordinary differential equations this paper describes a method that enables the user to construct systematically the set of all discrete point symmetries of a given ordinary differential equation ode of order two or greater provided that the ode has at least a one parameter lie group of point symmetries the method is easy to use and is based upon lie s method of constructing continuous symmetries the calculations are simple and computer algebra is not usually required various examples are used to illustrate the method the paper concludes with a proof that every ode whose lie group of point symmetries is isomorphic to the unimodular group has at least four inequivalent real discrete point symmetries

on the systematic approach to the classification of differential equations by group theoretical methods complete symmetry groups enable one to characterise fully a given differential equation by considering the reversal of an approach based upon complete symmetry groups we construct new classes of differential equations which have the equations of bateman monge ampere and born infeld as special cases we develop a symbolic algorithm to decrease the complexity of the calculations involved

on differential equations characterized by their lie point symmetries we study the geometry of differential equations determined uniquely by their point symmetries that we call lie remarkable we determine necessary and sufficient conditions for a differential equation to be lie remarkable furthermore we see how in some cases lie remarkability is related to the existence of invariant solutions we apply our results to minimal submanifold equations and to monge ampere equations in two independent variables of various orders

first integrals and reduction of a class of nonlinear higher order ordinary differential equations abstract we propose a method for constructing first integrals of higher order ordinary differential equations in particular third fourth and fifth order equations of the form x n h x x n 1 x are considered the relation of the proposed method to local and nonlocal symmetries are discussed

construction of trellis codes with a good distance profile systematic feedforward trellis codes for 8 psk and 16 qam modulation are constructed using a nested step by step algorithm which guarantees a good distance profile this makes the codes suitable for use with sequential decoding where a rapidly growing distance profile is needed to reduce the average number of computations in addition to having a good distance profile the new codes achieve asymptotic coding gains of up to 6 53 db a procedure based upon the fano 1963 algorithm fa is used to calculate the free distance of the new codes this procedure is very effective for finding the free distances of long trellis codes because of the computational and storage efficiency of the fa from a comparison of the new systematic feedforward codes with ungerboeck s 1982 1987 systematic feedback codes the authors conjecture that a systematic feedforward code of constraint length 2 spl nu can achieve the same free distance as a systematic feedback code of constraint length spl nu

lie group symmetry analysis of transport in porous media with variable transmissivity abstract we determine the lie group symmetries of the coupled partial differential equations governing a novel problem for the transient flow of a fluid containing a solidifiable gel through a hydraulically isotropic porous medium assuming that the permeability k of the porous medium is a function of the gel concentration c we determine a number of exact solutions corresponding to the cases where the concentration dependent permeability is either arbitrary or has a power law variation or is a constant each case admits a number of distinct lie symmetries and the solutions corresponding to the optimal systems are determined some typical concentration and pressure profiles are illustrated and a specific moving boundary problem is solved and the concentration and pressure profiles are displayed

symmetry analysis of initial value problems symmetry analysis is a powerful tool that enables the user to construct exact solutions of a given differential equation in a fairly systematic way for this reason the lie point symmetry groups of most well known differential equations have been catalogued it is widely believed that the set of symmetries of an initial value problem or boundary value problem is a subset of the set of symmetries of the differential equation the current paper demonstrates that this is untrue indeed an initial value problem may have no symmetries in common with the underlying differential equation the paper also introduces a constructive method for obtaining symmetries of a particular class of initial value problems

isospectral euler bernoulli beams with continuous density and rigidity functions isospectral systems are those that have exactly the same free vibration frequency spectrum with respect to a given boundary condition configuration in this paper seven different classes of inhomogeneous euler bernoulli beams with continuous density and flexural rigidity functions are found that are analytically solvable and that are isospectral with a homogeneous beam in the clamped clamped configuration of these exact solutions one class is isospectral with the homogeneous case in all ten distinct configurations obtainable from clamped sliding and two antiresonant end conditions whereas another class is isospectral in the six configurations with clamped hinged or free end conditions a connection with inverse problems is discussed