an upper bound on the aperiodic autocorrelation function for a maximal length sequence corresp the magnitude of the out of phase aperiodic autocorrelation function for a maximal length linear feedback shift register sequence of period n is at most 1 2 pi n 1 1 2 ln 4n pi previously the best upper bound was n 1 1 2 ln en

scalar product of bethe vectors from functional equations in this work the scalar product of bethe vectors for the six vertex model is studied by means of functional equations the scalar products are shown to obey a system of functional equations originated from the yang baxter algebra and its solution is given as a multiple contour integral

explicit merit factor formulae for fekete and turyn polynomials we give explicit formulas for the l 4 norm or equivalently for the merit factors of various sequences of polynomials related to the fekete polynomials

importance of convection and damping on rates of convergence for the lax wendroff method it is well known that in solving steady state problems using hyperbolic time stepping methods the intent is to drive the transients to zero as quickly as possible in this paper the convergence to steady state of the lax wendroff method applied to solving the equations of gas dynamics is analyzed for the laval nozzle problem by comparing the relative rates of damping and convection using a linearized eigenmode analysis this analysis is developed for the simpler isenthalpic system and then extended to the full euler equations finally this allows a comparison between these systems for both models useful analytical information can be gleaned about the transient behavior of these systems especially in regard to quantifying the competitive factors affecting the removal of unsteady waves

the merit factor of legendre sequences corresp turyn has shown by numerical computation that the merit factor of long legendre sequences offset by a quarter of their length has in all likelihood the asymptotic value 6 the ergodicity postulate is used in this correspondence to calculate that the merit factor f of a legendre sequence offset by a fraction f of its length has an asymptotic value given by 1 f 2 3 4 f 8f 2 f leq 1 2 which gives f 6 for f 1 4

a new search for skewsymmetric binary sequences with optimal merit factors previous results on skewsymmetric sequences with low autocorrelation obtained by making exhaustive searches for sequences with optimal merit factor are extended up to length 69 a sieve that required both the symmetric and antisymmetric components of a skewsymmetric sequence to have high merit factor to make limited searches up to length 117 was used and many sequences with merit factor greater than 9 were found

the peak sidelobe level of families of binary sequences a numerical investigation is presented for the peak sidelobe level psl of legendre sequences maximal length shift register sequences m sequences and rudin shapiro sequences the psl gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a binary sequence the growth of the psl of these infinite families of binary sequences is tested against the desired growth rate o spl radic nlnn for sequence length n the claim that the psl of m sequences grows like o spl radic n which appears frequently in the radar literature is concluded to be unproven and not currently supported by data notable similarities are uncovered between the psl and merit factor behavior under cyclic rotations of the sequences

rudin shapiro like polynomials in l 4 we examine sequences of polynomials with 1 1 coefficients constructed using the iterations p x p x x d 1 p x where d is the degree of p and p is the reciprocal polynomial of p if po 1 these generate the rudin shapiro polynomials we show that the l4 norm of these polynomials is explicitly computable we are particularly interested in the case where the iteration produces sequences with smallest possible asymptotic l4 norm or equivalently with largest possible asymptotic merit factor the rudin shapiro polynomials form one such sequence we determine all p 0 of degree less than 40 that generate sequences under the iteration with this property these sequences have asymptotic merit factor 3 the first really distinct example has a p 0 of degree 19

a fast time accurate unsteady full potential scheme resolution de l equation de potentiel par une methode implicite basee sur une factorisation approchee on presente des resultats pour des ecoulements sur des profils stationnaires et instationnaires a differents nombres de mach

improvements and extensions to a full potential formulation based on independent fields the paper presents a full potential model for nonisentropic unsteady transonic flows extending a parent formulation based on an independent approximation of the density and velocity potential fields it retains the advantage of the existence of a velocity potential while granting a unique solution by combining a correction of the stagnation pressure behind a shock with a new form of kutta condition the solution procedure relies on an unstructured node based finite volume approximation with linear shape functions and nonreflecting far field boundary conditions animproved upwind density biasing allows the solution in supersonic regions to bestabilized a new proof is given for the linearized unconditional stability of the implicit solver adopted for subsupersonic asymptotic conditions numerical results show that the method can model euler solutions more accurately than an isentropic full potential formulation for both steady and unsteady conditions applications to asymptotically supersonic flows complete the numerical validation

the cross correlation of binary sequences with optimal autocorrelation binary sequences with low correlation have applications in communication systems and cryptography though binary sequences with optimal autocorrelation were constructed in the literature no pair of binary sequences with optimal autocorrelation are known to have also best possible cross correlation in this paper new bounds on the cross correlation of binary sequences with optimal autocorrelation are derived and pairs of binary sequences having optimal autocorrelation and meeting some of these bounds are presented these new bounds are better than the sarwate bounds on the cross correlation of binary sequences with optimal autocorrelation

rudin shapiro like sequences with maximum asymptotic merit factor borwein and mossinghoff investigated the rudin shapiro like sequences which are infinite families of binary sequences usually represented as polynomials each family of rudin shapiro like sequences is obtained from a starting sequence which we call the seed by a recursive construction that doubles the length of the sequence at each step and many sequences produced in this manner have exceptionally low aperiodic autocorrelation borwein and mossinghoff showed that the asymptotic autocorrelation merit factor for any such family is at most 3 and found the seeds of length 40 or less that produce the maximum asymptotic merit factor of 3 the definition of rudin shapiro like sequences was generalized by katz lee and trunov to include sequences with arbitrary complex coefficients among which are families of low autocorrelation polyphase sequences katz lee and trunov proved that the maximum asymptotic merit factor is also 3 for this larger class here we show that a family of such rudin shapiro like sequences achieves asymptotic merit factor 3 if and only if the seed is either of length 1 or is the interleaving of a pair of golay complementary sequences for small seed lengths where this is not possible the optimal seeds are interleavings of pairs that are as close as possible to being complementary pairs and the idea of an almost complementary pair makes sense of remarkable patterns in previously unexplained data on optimal seeds for binary rudin shapiro like sequences

optimal odd length binary z complementary pairs a pair of sequences is called a golay complementary pair gcp if their aperiodic auto correlation sums are zero for all out of phase time shifts existing known binary gcps only have even lengths in the form of 21026 where are non negative integers to fill the gap left by the odd lengths we investigate the optimal oddlength binary pairs which display the closest correlation property to that of gcps our criteria of closeness is that each pair has the maximum possible zero correlation zone zcz width and minimum possible out of zone aperiodic auto correlation sums such optimal pairs are called optimal odd length binary z complementary pairs ob zcp in this paper we show that each optimal ob zcp has maximum zcz width of n 1 2 and minimum out of zone aperiodic sum magnitude of 2 where n denotes the sequence length odd systematic constructions of such optimal op zcps are proposed by insertion and deletion of certain binary gcps which settle the 2011 li fan tang tu open problem positively the proposed optimal ob zcps may serve as a replacement for gcps in many engineering applications where odd sequence lengths are preferred in addition they give rise to a new family of base two almost difference families adf which are useful in studying partially balanced incomplete block design bibd index terms aperiodic correlation almost difference set ads almost difference families adf golay complementary pair gcp zero correlation zone zcz z complementary pair zcp

binary sequences with merit factor 6 3 a method is described for the construction of binary sequences of very long length and with asymptotic merit factor 6 3 the result is backed up by strong experimental evidence although no formal proof for the asymptote is known the sequences were found by kristiansen using a small deterministic search which we describe borwein choi and jedwab have independently identified a merit factor asymptote of 6 3421 after we became aware of their work we realized that the sequences we construct are more simply described as periodic extensions of periodically rotated legendre sequences

functional relations for the order parameters of the chiral potts model following the method of jimbo miwa and others we obtain functional relations for the order parameters of the chiral potts model we have not yet solved these relations here we discuss their properties and show how one should beware of spurious solutions

the merit factor of binary sequences related to difference sets long binary sequences related to cyclic difference sets are investigated among all known constructions of cyclic difference sets it is shown that only sequences constructed from hadamard difference sets can have an asymptotic nonzero merit factor maximal length shift register sequences legendre and twin prime sequences are all constructed from hadamard difference sets the authors prove that the asymptotic merit factor of any maximal length shift register sequence is three for twin prime sequences it is shown that the best asymptotic merit factor is six this value is obtained by shifting the twin prime sequence one quarter of its length it turns out that legendre sequences and twin prime sequences have similar behavior jacobi sequences are investigated on the basis of the jacobi symbol the best asymptotic merit factor is shown to be six through the introduction of product sequences it is argued that the maximal merit factor among all sequences of length n is at least six when n is large the authors also demonstrate that it is fairly easy to construct sequences of moderate composite length with a merit factor close to six

rogers ramanujan identities in the hard hexagon model the hard hexagon model in statistical mechanics is a special case of a solvable class of hard square type models in which certain special diagonal interactions are added the sublattice densities and order parameters of this class are obtained and it is shown that many rogers ramanujan type identities naturally enter the working

further exact solutions of the eight vertex sos model and generalizations of the rogers ramanujan identities the restricted eight vertex solid on solid sos model is an exactly solvable class of two dimensional lattice models to each sitei of the lattice there is associated an integer heightli restricted to the range 1 li r 1 the boltzmann weights of the model are expressed in terms of elliptic functions of period 2k and involve a parameter in an earlier paper we considered the case k r here we generalize those considerations to the case sk r s an integer relatively prime tor we are again led to generalizations of the rogers ramanujan identities

new bounds and optimal binary signature sets part ii aperiodic total squared correlation we derive new bounds on the aperiodic total squared correlation atsc of binary antipodal signature sets for any number of signatures k and any signature length l we then present optimal designs that achieve the new bounds for several k l cases as interesting arguably side results we show that individual maximal merit factor sequences for example barker sequences are single user atsc optimal while neither the familiar gold nor the kasami set designs are atsc optimal in general the atsc optimal signature set designs provided in this work are in this sense better suited for asynchronous and or multipath code division multiplexing applications

a convergent finite element formulation for transonic flow a finite element formulation for the full potential equation in the case of two dimensional transonic flow is presented the formulation is based on an optimal control approach developed by glowinski and pironneau the solution of the full potential equation is obtained by a minimization problem using a new compactness result it is possible to prove convergence for the solutions of the minimization problem the a priori assumption of existence and uniqueness of a weak solution of the full potential equation satisfying an entropy condition implies that the limit function must be the solution it is possible to extend the convergence result to the case of three dimensional transonic potential flow

low correlation sequences from linear combinations of characters pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that when compared with a random sequence pairs simultaneously achieve significantly lower mean square autocorrelation values for each sequence in the pair and significantly lower mean square crosscorrelation values if we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation and if we define demerit factor as the reciprocal of merit factor then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of 1 our constructions provide sequence pairs with a crosscorrelation demerit factor significantly less than 1 and at the same time the autocorrelation demerit factors of the individual sequences can also be made significantly less than 1 which also indicates better than average performance the sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters such as maximal linear recursive sequences m sequences and legendre sequences in this paper exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length

cyclotomic integers and finite geometry the most powerful method for the study of finite geometries with regular or quasiregular automorphism groups g is to translate their definition into an equation over the integral group ring 2 g and to investigate this equation by applying complex representations of g for the definitions and the basic facts see section 2 if g is abelian this approach boils down to proving or disproving the existence of elements of 2 g with 0 1 coefficients whose character values are cyclotomic integers of certain prescribed absolute values up to now there have been two general methods to tackle this problem namely hall s multiplier concept and turyn s selfconjugacy approach however both methods need severe technical assumptions and thus are not applicable to many classes of problems despite many efforts over a period of more than 30 years no general method has been found to overcome these difficulties in this paper we present a new approach to the study of combinatorial structures via group ring equations which works without any restrictive assumptions in order to understand the method of the present paper it will be instructive to briefly discuss the self conjugacy concept first turyn 51 demonstrated that the character method for the study of group ring equations works very nicely under the so called self conjugacy condition an integer n is called self conjugate modulo m if all prime ideals above n in the mth cyclotomic field q m are invariant under complex conjugation under this condition it is possible to find all cyclotomic integers in q m of absolute value nt 2 for any positive integer t it is the complete knowledge of the cyclotomic integers of prescribed absolute value which makes the character method work so well under the self conjugacy condition since turyn s fundamental work 51 there have been dozens of papers extending and refining his approach however all these results are restricted to the case of self conjugacy and that is a very severe restriction indeed namely the probability that n is selfconjugate modulo m decreases exponentially fast in the number of distinct prime divisors of n and m see remark 2 2 this means that the self conjugacy method fails in almost all cases one may ask if it is possible to extend turyn s method in order to get rid of the self conjugacy assumption it turns out that in general this is impossible at least with present day methods the required complete knowledge of the cyclotomic integers of prescribed absolute value would yield an

on the existence of the entropic solution for the transonic flow problem results contained in the presented paper are the further development of the paper by kloueek and netas l the spirit of the analysis for the psuedo time dependent approach is taken from the paper of friedman and netas 2 the nearest mathematical model bringing the problem of transonic flow within the framework of well established theory is the so called unsteady transonic flow problem the analysis of the existence and eventually the uniqueness of the solutions of the resulting nonlinear second order hyperbolic equation is still an open problem most of the numerical methods for the calculating of transonic flow can be rewritten in a form from which a successive iteration could be derived using an artificial time coordinate see e g jameson 3 4 hafez et al 5 typically one ends up with

a complete description of golay pairs for lengths up to 100 in his 1961 paper marcel golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 6 problem andres in his 1977 master s thesis developed an algorithm which reduced this to a 2 n 2 1 search and investigated lengths up to 58 for existence of pairs in this paper we describe refinements to this algorithm enabling a 2 n 2 5 search at length 82 we find no new pairs at the outstanding lengths 74 and 82 in extending the theory of composition we are able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n combining this with the results of searches at all allowable lengths up to 100 we identify five primitive pairs all others pairs of lengths less than 100 may be derived using the methods outlined

numerical results and stability analysis for the computation of the transonic flow problems using an artificial time formulation abstract a numerical method for the computation of the entropic solution for transonic flow is developed and studied within the use of the pseudo time formulation stability for t 0 is provided finite element implementation of the artificial compressibility method and time dependent treatment of the kutta joukowski condition are included test examples of the flow around naca 0012 and rae 2822 airfoils for supercritical flows are presented

merit factor of chu sequences and best merit factor of polyphase sequences chu sequences are a family of polyphase sequences that have perfect periodic autocorrelations and good aperiodic autocorrelations it has previously been proved that the maximum offpeak aperiodic autocorrelation in absolute value of the chu sequence of length n is asymptotically equal to 0 480261 n it has also been empirically observed that the merit factor of chu sequences appears to grow like a constant times n in this note we provide an analytic proof that the merit factor of the chu sequence of length n is bounded below by a constant multiple of n for all n to the author s knowledge this is the first time a family of polyphase sequences of all lengths has been proved to have merit factor growing at least like order n

exhaustive search for low autocorrelation binary sequences binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as ground states of the bernasconi model computer searches are the main tool in the construction of such sequences owing to the exponential size of the configuration space exhaustive searches are limited to short sequences we discuss an exhaustive search algorithm with run time characteristic and apply it to compile a table of exact ground states of the bernasconi model up to n 48 the data suggest f 9 for the optimal merit factor in the limit

generating fluttering patterns with low autocorrelation for coded exposure imaging the performance of coded exposure imaging critically depends on finding good binary sequences previous coded exposure imaging methods have mostly relied on random searching to find the binary codes but that approach can easily fail to find good long sequences due to the exponentially expanding search space in this paper we present two algorithms for generating the binary sequences which are especially well suited for generating short and long binary sequences respectively we show that the concept of low autocorrelation binary sequences which has been successfully exploited in the field of information theory can be applied to generate shutter fluttering patterns we also propose a new measure for good binary sequences based on the new measure we introduce two new algorithms for coded exposure imaging a modified legendre sequence method and a memetic algorithm experiments using both synthetic and real data show that our new algorithms consistently generate better binary sequences for the coded exposure problem yielding better deblurring and resolution enhancement results compared to previous methods of generating the binary codes

polyphase power residue sequences polyphase versions of the well known binary legendre or quadratic residue sequences were first described and analysed by sidelnikov over thirty years ago but have since received very little attention here it is shown that these q phase sequences of prime length l can also be constructed from the index sequence of length l or equivalently from the cosets of q th power residues and non residues these sequences are also shown to fall into two classes each of which has well defined periodic autocorrelation functions and merit factors class i sequences exist for prime l q 1 mod 2 q and q even whereas class ii sequences correspond to primes of the form l 1 mod 2 q and are available for all values of q class i sequences have complex out of phase correlation values with magnitudes less than or equal to 5 whereas for class ii sequences these are purely real with magnitude less than or equal to 3 some other properties are also investigated

dynamical approach study of spurious steady state numerical solutions of nonlinear differential equations i the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics abstract the goal of this paper is to utilize the theory of nonlinear dynamics approach to investigate the possible sources of errors and slow convergence and nonconvergence of steady state numerical solutions when using the time dependent approach for nonlinear hyperbolic and parabolic partial differential equations terms this interdisciplinary research belongs to a subset of a new field of study in numerical analysis sometimes referred to as the dynamics of numerics and the numerics of dynamics at the present time this new interdisciplinary topic is still the property of an isolated discipline with all too little effort spent in pointing out an underlying generality that could make it adaptable to diverse fields of applications this is the first of a series of research papers under the same topic our hope is to reach researchers in the fields of computational fluid dynamics cfd and in particular hypersonic and combustion related cfd by simple examples in which the exact solutions of the governing equations are known the application of the apparently straightforward numerical technique to genuinely nonlinear problems can be shown to lead to incorrect or misleading results one striking phenomenon is that with the same initial data the continuum and its discretized counterpart can asymptotically approach different stable solutions this behavior is especially important for employing a time dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used with the unique property of the different dependence of the solution on initial data for the partial differential equation and the discretized counterpart it is not easy to delineate the true physics from numerical artifacts when numerical methods are the sole source of solution procedure for the continuum part i concentrates on the dynamical behavior of time discretization for scalar nonlinear ordinary differential equations in order to motivate this new yet unconventional approach to algorithm development in cfd and to serve as an introduction for parts 11 and iii of the same series of research papers

modifications of modified jacobi sequences the known families of binary sequences having asymptotic merit factor 6 0 are modifications to the families of legendre sequences and jacobi sequences in this paper we show that at n pq there are many suitable modifications other than the jacobi or modified jacobi sequences furthermore we will give three new modifications to the character sequences of length n pq based on these new modifications for any pair of large p and q we can construct a binary sequence of length 2pq so that such families of sequences have asymptotic merit factor 6 0 without cyclic shifting of the base sequences

multiple solutions of the transonic potential flow equation the two dimensional transonic potential flow equation when solved in discrete form for steady flow over an airfoil has been found to yield more than one solution in certain bands of angle of attack and mach number the most striking ex ample of this is the appearance of nonsymmetric solutions with large positive or negative lift for symmetric airfoils at zero angle of attack the behavior of these anomalous solutions is exam ined as grid size is varied by large factors and found to be not qualitatively different from that of ormalrf solutions outside the nonuniqueness band thus it appears that the effect is not due to discretization error and that the basic tran sonic potential flow partial differential equation admits nonunique solutions for certain values of angle of attack and mach number

sequence pairs with asymptotically optimal aperiodic correlation the pursley sarwate criterion of a pair of finite complex valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic cross correlations of the two sequences it is known that this quantity is always at least 1 with equality if and only if the sequence pair is a golay pair we exhibit pairs of complex valued sequences whose entries have unit magnitude for which the pursley sarwate criterion tends to 1 as the sequence length tends to infinity our constructions use different carefully chosen chu sequences

some hyperelliptic function identities that occur in the chiral potts model we present a number of hyperelliptic function identities that occur in the chiral potts model some of these are relevant to the outstanding problem of solving the functional relations for the order parameter

functional relations for the order parameters of the chiral potts model low temperature expansions abstract this is the third in a series of papers in which we set up and discuss the functional relations for the split rapidity line correlation function in the n state chiral potts model the order parameters of the model can be obtained from this function here we consider the case n 3 and write the equations explicitly in terms of the hyperelliptic functions parametrization we also present four term low temperature series expansions which we hope will cast light on the analyticity properties needed to solve the relations the problem remains unsolved but we hope that this will prove to be a step in the right direction

on binary probing signals and instrumental variables receivers for radar the so called merit factor approach mfa to radar binary sequence design has led to several theoretical contributions in fairly diverse research areas including information theory computer science combinatorial optimization and analytical number theory however the mfa which basically aims at minimizing the clutter effect on radar performance implicitly assumes the use of a least squares ls receiver that is optimal only when there is no clutter this problem can be eliminated by using a more general optimal instrumental variables iv receiver in lieu of the ls receiver the iv receiver can reject clutter more efficiently than the ls receiver additionally the binary sequence design problem associated with the iv approach has an interesting form

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

aperiodic crosscorrelation of sequences derived from characters it is shown that the pairs of maximal linear recursive sequences m sequences typically have mean square aperiodic crosscorrelation on par with that of random sequences but that if one takes a pair of m sequences where one is the reverse of the other and shifts them appropriately one can get significantly lower mean square aperiodic crosscorrelation sequence pairs with even lower mean square aperiodic crosscorrelation are constructed by taking a legendre sequence cyclically shifting it and then cutting it approximately in half and using the halves as the sequences of the pair in some of these constructions the mean square aperiodic crosscorrelation can be lowered further if one truncates or periodically extends appends the sequences exact asymptotic formulas for mean squared aperiodic crosscorrelation are proved for sequences derived from additive characters including m sequences and modified versions thereof and multiplicative characters including legendre sequences and their relatives data are presented that show that the sequences of modest length have performance that closely approximates the asymptotic formulas

determination of the merit factor of legendre sequences m j e golay ibid vol it 23 no 1 p 43 51 1977 has used the ergodicity postulate to calculate that the merit factor f of a legendre sequence offset by a fraction f of its length has an asymptotic value given by 1 f 2 3 4 mod f mod 8f sup 2 mod f mod

the merit factor of long low autocorrelation binary sequences corresp the asymptotic merit factor i e the ratio of central to sidelobe energy of extremely long optimally iow autocorrelation sequences formerly calculated as 2e 2 14 778 cdots with the use of an ergodicity hypothesis and a convenient but faulty approximation is recalculated without that approximation and is established at 12 32 cdots

on the search for good aperiodic binary invertible sequences for an aperiodic invertible sequence of length l the optimality criterion is chosen to be the minimum noise enhancement factor of the corresponding aperiodic inverse filter the noise enhancement factor is defined as the ratio of the noise energies at the outputs of the aperiodic inverse and the normalized matched filters of the sequence due to white noise at the filter inputs optimal binary sequences of length l spl les 32 and optimal binary skew symmetric sequences of length 33 spl les l spl les 59 were found by exhaustive search the search for near optimal sequences is shown to have strong connections to the search for sequences with large products of golay 1977 merit factor times the minimum of the energy density spectrum based on legendre sequences and on kronecker product sequences long near optimal binary sequences are found that have associated noise enhancement factors close to 1 db

transonic vortex flows past delta wings integral equation approach the steady full potential equation is written in the form of poisson s equation and the solution of the velocity field is expressed in terms of an integral equation the solution consists of a surface integral of vorticity distribution on the wing and its free vortex sheets and a volume integral of source distribution within a volume around the wing and its free vortex sheets the solution is obtained through successive iteration cycles the density gradient in the source distribution is computed by using a type differencing scheme the method is applied to delta wings and the numerical examples show that a curved shock is captured on the suction side of the wing it is attached to the lower surface of the leading edge vortex but does not necessarily reach the wing surface the present solution does not suffer from the numerical diffusion problem usually encountered with the finite difference solutions of euler equations

a riemann problem in gas dynamics with bifurcation abstract we construct the solution of the riemann problem for 2 2 isothermal gas dynamics in a duct with discontinuous diameter besides shocks and rarefaction there are standing waves the solution exists globally it is obtained as an asymptotic solution for an appropriate cauchy problem with continuous data in certain cases bifurcation occurs and there are three solutions one of which is unstable this is an example of a riemann problem whose solution depends discontinuously on the initial data

corner transfer matrices of the chiral potts model ii the triangular lattice we consider a two dimensional edge interaction model satisfying the star triangle relations for the triangular lattice the corner transfer matrices are functions of three rapidities we show that they possess various factorization properties and satisfy certain equations we indicate how these equations can be solved for the ising model we then consider the three state chiral potts model and obtain low temperature solutions to the equations the conjectured formula for the order parameter the spontaneous magnetization is verified to one more order in a series expansion

littlewood polynomials with small l4 norm abstract littlewood asked how small the ratio f 4 f 2 where denotes the l norm on the unit circle can be for polynomials f having all coefficients in 1 1 as the degree tends to infinity since 1988 the least known asymptotic value of this ratio has been 7 6 4 which was conjectured to be minimum we disprove this conjecture by showing that there is a sequence of such polynomials derived from the fekete polynomials for which the limit of this ratio is less than 22 19 4

binary sequences with merit factor greater than 6 34 the maximum known asymptotic merit factor for binary sequences has been stuck at a value of 6 since the 1980s several authors have suggested that this value cannot be improved in this paper we construct an infinite family of binary sequences whose asymptotic merit factor we conjecture to be greater than 6 34 we present what we believe to be compelling evidence in support of this conjecture the numerical experimentation that led to this construction is a significant part of the story

an implicit lambda scheme this paper is concerned with the numerical simulation of transonic inviscid flows the unsteady euler equations are written in characteristi c type variables discretized in time and solved by means of an implicit technique or an alternating direction implicit technique for one and two dimensional flows respectively so that only block tridiagonal systems have to be solved at each time level the present method has been successfully applied to one dimension al transonic internal flows and two dimensional transonic external flows within the framework of thin airfoil theory and can be generalized to transonic two and three dimensional flows for arbitrary geometries in all computed cases the present technique has proved itself reliable and about one order of magnitude more efficient than its well known explicit counterpart

aperiodic correlations and the merit factor of a class of binary sequences corresp a class of binary sequences of length n 2 m is considered and it is shown that their aperiodic autocorrelations can be calculated recursively in a simple way based on this the merit factor of the sequences is calculated and it is shown that the asymptotic value is 3 finally it is proved that the magnitude of the maximal aperiodic autocorrelation is bounded by n 0 9

the distribution of general gauss sums and similar arithmetic functions at prime arguments on axiomatise les arguments donnes par heath brown et patterson 1979 jusqu a une extension donnee afin de les rendre applicables a des fonctions arithmetiques autres que les sommes de gauss

construction of even length binary sequences with asymptotic merit factor 6 starting with the family of legendre sequences of length p parker constructed a new family of binary sequences of length 2p with good negacyclic correlation properties computer calculations indicated that the asymptotic merit factor of his family is 6 in this correspondence a simple version of parker s construction is given and further applied to jacobi and modified jacobi sequences it is then proven that each of the families constructed including parker s has asymptotic merit factor 6

multi image deblurring using complementary sets of fluttering patterns we present a novel coded exposure video technique for multi image motion deblurring the key idea of this paper is to capture video frames with a set of complementary fluttering patterns which enables us to preserve all spectrum bands of a latent image and recover a sharp latent image to achieve this we introduce an algorithm for generating a complementary set of binary sequences based on the modern communication theory and implement the coded exposure video system with an off the shelf machine vision camera to demonstrate the effectiveness of our method we provide in depth analyses of the theoretical bounds and the spectral gains of our method and other state of the art computational imaging approaches we further show deblurring results on various challenging examples with quantitative and qualitative comparisons to other computational image capturing methods used for image deblurring and show how our method can be applied for protecting privacy in videos

efficient optimization of the merit factor of long binary sequences autocorrelation sidelobes are a form of self noise that reduce the effectiveness of phase coding in radar and communication systems the merit factor is a well known measure related to the autocorrelation sidelobe energy of a sequence in this paper an equation is derived that allows the change in the merit factor of a binary sequence to be computed for all single element changes with o nlogn operations where n is the sequence length the approach is then extended to multiple element changes allowing the merit factor change to be calculated with an additional o ns3 operations where nsis the number of changed elements irrespective of sequence length the multiple element calculations can be used to update the single element calculations so that in iterative use only o n operations are required per element change to keep the single element calculations current a steep descent algorithm a variation on the steepest descent method employing these two techniques was developed and applied to quarter rotated periodically extended legendre sequences producing optimized sequences with an apparent asymptotic merit factor of approximately 6 3758 modestly higher than the best known prior result of approximately 6 3421 modified jacobi sequences improve after steep descent to an approximate asymptotic merit factor of 6 4382 three prime and four prime jacobi sequences converge very slowly making a determination difficult but appear to have a higher post steep descent asymptotic merit factor than legendre or modified jacobi sequences

the baxter revolution i review the revolutionary impact rodney baxter has had on statistical mechanics beginning with his solution of the 8 vertex model in 1971 and the invention of corner transfer matrices in 1976 to the creation of the rsos models in 1984 and his continuing current work on the chiral potts model