golay complementary sequence sets with large zero correlation zones zero correlation zone zcz sequence sets and golay complementary sets gcss have different correlation properties and hence have different engineering applications a number of constructions of zcz sequence sets and gcss have been proposed respectively in the literature in addition some zcz sequence sets can be constructed from mutually orthogonal gcss in this paper the relationship between gcss and zcz sets is discovered further we propose a new type of sequence sets which are zcz sequence sets and also gcss they are called the golay zcz sequence sets in this paper therefore they have low peak to average power ratios when employed in ofdm systems due to the good autocorrelation properties of gcss besides the golay zcz sets possess zero autocorrelations and cross correlations within their zcz and hence have the potential application to synchronization furthermore a construction of golay zcz sequence family with flexible set sizes various sequence lengths and large zcz widths is proposed in this paper

quantum distribution functions for radial observables for quantum systems with two dimensional configuration space we construct a physical radial momentum observable rescaling the radius we find that the dilation degrees of freedom form a weyl algebra with this we construct a radial wigner quasiprobability distribution function

comments on a new construction of 16 qam golay complementary sequences and extension for 64 qam golay sequences for original article by c v chong see ibid vol 49 no 11 p 2953 2959 nov 2003 some corrections are given for the sequence pairing descriptions of 16 qam golay complementary sequences in chong venkataramani and tarokh s paper together with a related correction for lee and golomb s 64 qam golay sequence construction lee and golomb obtained 496 808 and 976 offset pairs for length 2m 64 qam golay sequences m 2 3 4 we obtained 724 972 and 1224 offset pairs adding w 1 to case iii in lee and golomb s construction gives some additional offset pairs others are new and exist for m ges 3 only descriptions of new offset pairs and enumeration for all first order offset pairs are proposed as conjectures an example is given to show that there exist other 64 qam golay sequences not within this construction

hydrogen atom in phase space the wigner representation the hydrogen atom is a fundamental exactly soluble system for which the wigner function being a quantum analogue of the joint probability distribution of position and momentum is unknown in this paper we present an effective method of calculating the wigner function for all bound states of the nonrelativistic hydrogen atom the formal similarity between the eigenfunctions of the nonrelativistic hydrogen atom in the momentum representation and the klein gordon propagator has allowed the calculation of the wigner function for an arbitrary bound state of the hydrogen atom using a simple atomic integral as a generator these wigner functions for some low lying states are depicted and discussed

wigner function for the radial equation of the coulomb problem in langer space in this paper a theoretical study of the coulomb problem in quantum phase space is reported the langer coordinate transformation is used to map the coulomb problem into a one dimensional morse oscillator as a result the wigner distribution functions for the morse oscillator are obtained the form of these functions is presented for a few principal quantum number n and the angular momentum quantum number l the results obtained correspond to the solution of the coulomb problem in the spherical coordinate system

the lp boundedness of wave operators for schrodinger operators with threshold singularities abstract let h v be a schrodinger operator on l 2 r n with real valued potential v for n 4 and let h 0 if v has sufficiently rapid decay the wave operators defined as w s lim t e i t h e i t h 0 are known to be bounded on l p r n for all 1 p if zero is not an eigenvalue and on 1 p n 2 if zero is an eigenvalue we show that these wave operators are also bounded on l 1 r n by direct examination of the integral kernel of the leading term furthermore if r n v x x d x 0 for all eigenfunctions then the wave operators are l p bounded for 1 p n if in addition r n x v x x d x 0 then the wave operators are bounded for 1 p

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

shared autocorrelation property of sequences due to the low peak to mean envelope power ratio pmepr of golay sequences together with their connection to generalized reed muller codes many authors have proposed using golay sequences as codewords in orthogonal frequency division multiplexing ofdm golay sequences that unexpectedly share the same aperiodic autocorrelation function can be used to construct longer golay sequences we study the shared autocorrelation property of general sequences with the ultimate goal of using those results to find other low power sequences in this paper we provide several new constructions of families of pairs of sequences with the shared autocorrelation property that enable us to explain nearly all of the binary shared autocorrelation property for sequences of lengths up to 24

on the computation and reduction of the peak to average power ratio in multicarrier communications for any code c defined over an equal energy constellation it is first shown that at any time instance the problem of determining codewords of c with high peak to average power ratios papr in a multicarrier communication system is intimately related to the problem of minimum distance decoding of c subsequently a method is proposed for computing the papr by minimum distance decoding of c at many points of time moreover an upper bound on the error between this computed value and the true one is derived analogous results are established for codes defined over arbitrary signal constellations as an application of this computational method an approach for reducing the papr of c proposed by jones and wilkinson 1996 is revisited this approach is based on introducing a specific phase shift to each coordinate of all the codewords where phase shifts are independent of the codewords and known both to the transmitter and the receiver we optimize the phase shifts offline by applying our method for computing the papr for the coding scenario proposed by the etsi bran standardization committee reductions of order 4 5 db can be freely obtained using the computed phase shifts examples are provided showing that most of the gain is preserved when the computed optimal phase shifts are rounded to quantenary phase shift keying psk 8 psk and 16 psk type phase shifts

complementary sets of non power of two length for peak to average power ratio reduction in ofdm golay complementary sequences and complementary sets have been proposed to deal with the high peak to average power ratio papr problem in orthogonal frequency division multiplexing ofdm system the existing constructions of complementary sets based on generalized boolean functions are limited to lengths which are powers of two in this paper we propose novel constructions of binary and nonbinary complementary sets of non power of two length regardless of whether or not the length of the complementary set is a power of two its papr is still upper bounded by the size of the complementary set therefore the constructed complementary sets can be applied in practical ofdm systems where the number of used subcarriers is not a power of two in addition while the binary golay complementary pairs exist only for limited lengths the constructed binary complementary sets of size 4 exist for more lengths with papr at most 4

novel 16 qam and 64 qam near complementary sequences with low pmepr in ofdm systems in this paper we first propose a novel construction of 16 quadrature amplitude modulation qam near complementary sequences with low peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm systems the proposed 16 qam near complementary sequences can be constructed by utilizing novel nonlinear offsets where the length of the sequences is n 2 m the family size of the newly constructed 16 qam near complementary sequences is 8 times m 2 times 4 m 1 and the pmepr of these sequences is proven to satisfy pmepr 2 4 thus the proposed construction can generate a number of 16 qam near complementary sequences with low pmepr resulting in the improvement of the code rate in ofdm systems furthermore we also propose a novel construction of 64 qam near complementary sequences with low pmepr which is the first proven construction of 64 qam near complementary sequences the pmeprs of two types of the proposed 64 qam near complementary sequences are proven to satisfy that pmepr 3 62 or pmepr 2 48 respectively the family size of the newly constructed 64 qam near complementary sequences is 64 times m 2 times 4 m 1

a construction of ofdm 16 qam sequences having low peak powers using a realization of 16 qam as set addition of two scaled versions of the 4 psk constellation we construct 16 qam sequences having low peak to mean envelope power ratios pmepr from 4 psk golay sequences various upper bounds on the peak envelope powers of these sequences are established transmission using these sequences provides twice as much rate as transmission using complementary golay sequences with a maximum pmepr of 3 6 5 56 db

complementary sets generalized reed muller codes and power control for ofdm the use of error correcting codes for tight control of the peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm transmission is considered in this correspondence by generalizing a result by paterson it is shown that each q phase q is even sequence of length 2m lies in a complementary set of size 2k 1 where k is a nonnegative integer that can be easily determined from the generalized boolean function associated with the sequence for small k this result provides a reasonably tight bound for the pmepr of q phase sequences of length 2 m a new 2h ary generalization of the classical reed muller code is then used together with the result on complementary sets to derive flexible ofdm coding schemes with low pmepr these codes include the codes developed by davis and jedwab as a special case in certain situations the codes in the present correspondence are similar to paterson s code constructions and often outperform them

a systematic framework for the construction of optimal complete complementary codes the complete complementary code ccc that was proposed by suehiro and hatori is a sequence family that is a set of sequence sets with ideal correlation sums numerous studies in the literature show its applications to direct spread code division multiple access ds cdma systems for interchannel interference ici free communication with improved spectral efficiency in this paper we propose a systematic framework for the construction of cccs based on n shift cross orthogonal sequence families n co sfs we show theoretical bounds on the size of n co sfs and cccs and give a set of four algorithms for their generation and extension the algorithms are optimal in the sense that the size of the resultant sequence families achieves theoretical bounds and with the algorithms we can construct an optimal ccc consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence sets we also discuss the family size alphabet size and length of constructible cccs based on the proposed algorithms

new constructions of general qam golay complementary sequences a construction of general quadrature amplitude modulation qam golay complementary sequences based on quadrature phase shift keying golay davis jedwab sequences gdj sequences is described existing constructions of 16 and 64 qam golay sequences are extended to 4q qam sequences of length 2m for q 1 m 2 this construction gives m 1 42 q 1 m 1 4 q 1 2q 1 m 2 4 m 1 golay complementary sequences a previous offset pair enumeration conjecture for 64 qam golay sequences is proved as a special case of the enumeration for 4q qam golay sequences when used for orthogonal frequency division multiplexing signals the peak to mean envelope power ratio upper bound is shown to be 6 2q 1 2q 1 approaching 6 as the qam constellation size increases

how do more golay sequences arise in 1999 davis and jedwab gave a direct construction of golay complementary sequences over zopf2 h of length 2 m recently li and chu found 1024 more quaternary golay complementary sequences of length 16 that cannot be obtained by the direct construction using exhaustive computer enumeration it is shown how these sequences arise from interleaving and concatenation of two classes of golay complementary sequences given as an example by davis and jedwab these examples spawn new golay sequences over zopf2 h of length 2m for all h ges 2 and m ges 4

a new construction of 16 qam golay complementary sequences we present a new construction of 16 qam golay sequences of length n 2 sup m the number of constructed sequences is 14 12m m 2 4 sup m 1 when employed as a code in an orthogonal frequency division multiplexing ofdm system this set of sequences has a peak to mean envelope power ratio pmepr of 3 6 by considering two specific subsets of these sequences we obtain new codes with pmepr bounds of 2 0 and 2 8 and respective code sizes of 2 2m m 2 4 sup m 1 and 4 4m m 2 4 sup m 1 these are larger than previously known codes for the same pmepr bounds

simple strong glass forming models mean field solution with activation we introduce simple models inspired by previous models for froths and covalent glasses with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems these models are also a generalization of backgammon or urn models to a non constant number of particles where entropic barriers are replaced by energy barriers allowing for the existence of activated processes we formulate a mean field version of the models which keeps most of the features of the finite dimensional ones and solve analytically the out of equilibrium dynamics in the low temperature regime where activation plays an essential role

dispersive estimates for higher dimensional schrodinger operators with threshold eigenvalues i the odd dimensional case we investigate l1 rn l rn dispersive estimates for the schrodinger operator h v when there is an eigenvalue at zero energy and n 5 is odd in particular we show that if there is an eigenvalue at zero energy then there is a time dependent rank one operator ft satisfying ft l1 l t 2 n2 for t 1 such that eithpac ft l1 l t 1 n2 for t 1 with stronger decay conditions on the potential it is possible to generate an operator valued expansion for the evolution taking the form eithpac h t 2 n2a 2 t 1 n2a 1 t n2a0 with a 2 and a 1 finite rank operators mapping l1 rn to l rn while a0 maps weighted l1 spaces to weighted l spaces the leading order terms a 2 and a 1 vanish when certain orthogonality conditions between the potential v and the zero energy eigenfunctions are satisfied we show that under the same orthogonality conditions the remaining t n2a0 term also exists as a map from l1 rn to l rn hence eithpac h satisfies the same dispersive bounds as the free evolution despite the eigenvalue at zero

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

paraunitary based boolean generator for qam complementary sequences of length 2 k a boolean generator for a large number of standard complementary qam sequences of length 2 k is proposed this boolean generator is derived from the authors earlier paraunitary generator which is based on matrix multiplications both generators are based on unitary matrices in contrast to previous boolean qam algorithms which represent complementary sequences as a weighted sum our algorithm has a multiplicative form any element of a sequence can be generated efficiently by indexing the entries of unitary matrices with the binary representation of the discrete time index which is easily implemented as a binary counter our 1qum based on one qam unitary matrix and 2qum based on two qam unitary matrices algorithms generate generalized case i iii sequences and generalized case iv and v sequences respectively as specified by liu et al in 2013 in addition to many new 2qum sequences the ratio of the numbers of sequences that are generated by our new construction and the previous construction increases with the constellation size for example for a 1024 qam sequence of length 1024 this ratio is 4 4 however if we compare only 2qum sequences to case iv and v sequences this ratio is 267

on cosets of the generalized first order reed muller code with low pmepr golay sequences are well suited for use as codewords in orthogonal frequency division multiplexing ofdm since their peak to mean envelope power ratio pmepr in q ary phase shift keying psk modulation is at most 2 it is known that a family of polyphase golay sequences of length 2m organizes in m 2 cosets of a q ary generalization of the first order reed muller code rmq 1 m in this paper a more general construction technique for cosets of rm q 1 m with low pmepr is established these cosets contain so called near complementary sequences the application of this theory is then illustrated by providing some construction examples first it is shown that the m 2 cosets of rmq 1 m comprised of golay sequences just arise as a special case second further families of cosets of rmq 1 m with maximum pmepr between 2 and 4 are presented showing that some previously unexplained phenomena can now be understood within a unified framework a lower bound on the pmepr of cosets of rmq 1 m is proved as well and it is demonstrated that the upper bound on the pmepr is tight in many cases finally it is shown that all upper bounds on the pmepr of cosets of rmq 1 m also hold for the peak to average power ratio papr under the walsh hadamard transform wht

on the lp boundedness of wave operators for two dimensional schrodinger operators with threshold obstructions abstract let h v be a schrodinger operator on l 2 r 2 with real valued potential v and let h 0 if v has sufficient pointwise decay the wave operators w s lim t e i t h e i t h 0 are known to be bounded on l p r 2 for all 1 p if zero is not an eigenvalue or resonance we show that if there is an s wave resonance or an eigenvalue only at zero then the wave operators are bounded on l p r 2 for 1 p this result stands in contrast to results in higher dimensions where the presence of zero energy obstructions is known to shrink the range of valid exponents p

wigner function statistics in classically chaotic systems we have studied statistical properties of the values of the wigner function w x of 1d quantum maps on compact 2d phase space of finite area v for this purpose we have defined a wigner function probability distribution p w 1 v w w x dx which has by definition fixed first and second moments in particular we concentrate on relaxation of time evolving quantum states in terms of w x starting from a coherent state we have shown that for a classically chaotic quantum counterpart the distribution p w in the semiclassical limit becomes a gaussian distribution that is fully determined by the first two moments numerical simulations have been performed for the quantum sawtooth map and the quantized kicked top in a quantum system with hilbert space dimension n 1 the transition of p w to a gaussian distribution was observed at times t log n in addition it has been shown that the statistics of wigner functions of propagator eigenstates is gaussian as well in the classically fully chaotic regime we have also studied the structure of the nodal cells of the wigner function in particular the distribution of intersection points between the zero manifold and arbitrary straight lines

new 64 qam golay complementary sequences a construction of 64 qam golay complementary sequences was proposed by lee and golomb where three qpsk golay davis jedwab complementary sequences gdj sequences or standard golay sequences related by a pair of offsets were combined to form each 64 qam golay sequence feasible offset pairs were given as first order generalized boolean functions in algebraic normal form new offset pairs were described in a conjecture of li leading to new 64 qam golay complementary sequences the proof of the conjecture is presented

asymptotics of radial wave equations the langer modification is an improvement in the wkb analysis of the radial schrodinger equation we derive a generalization of the langer modification to any radial operator for differential operators we write the modified classical symbols explicitly and show that the wkb wavefunctions with the modification have the exact limiting behavior for small radius unlike in the schrodinger case generally the modified radial analysis is not equivalent to the wkb analysis of the full problem before reduction by the spherical symmetry

a framework for the construction ofgolay sequences in 1999 davis and jedwab gave an explicit algebraic normal form for m 2 2h m 1 ordered golay pairs of length 2mmiddot over z2h involving m 2 2h m 1 golay sequences in 2005 li and chu unexpectedly found an additional 1024 length 16 quaternary golay sequences fiedler and jedwab showed in 2006 that these new golay sequences exist because of a crossover of the aperiodic autocorrelation function of certain quaternary length eight sequences belonging to golay pairs and that they spawn further new quaternary golay sequences and pairs of length 2m for m 4 under budisin s 1990 iterative construction the total number of golay sequences and pairs spawned in this way is counted and their algebraic normal form is given explicitly a framework of constructions is derived in which turyn s 1974 product construction together with several variations plays a key role all previously known golay sequences and pairs of length 2m over z2h can be obtained directly in explicit algebraic normal form from this framework furthermore additional quaternary golay sequences and pairs of length 2m are produced that cannot be obtained from any other known construction the framework generalizes readily to lengths that are not a power of 2 and to alphabets other than z2h

a new construction of 64 qam golay complementary sequences in this correspondence we present a new construction for 64 qam golay sequences of length n 2 sup m for integer m the peak envelope power pep of 64 qam golay sequences is shown to be bounded by 4 66n the new construction of 64 qam golay sequences of length n 2 sup m is based on our earlier construction of new offsets of 16 qam golay sequences which are also presented here the total number of offsets of 64 qam golay sequences is 496 for m 2 808 for m 3 and 976 for m 4 obtained by computer search we also computed the pep distribution for 64 qam golay sequences for m 2 m 3 and m 4

on lp boundedness of wave operators for 4 dimensional schrodinger operators with threshold singularities abstractlet h v x be a schrodinger operator on l 2 r 4 h 0 assume that v x v x c x for some 8 let w s limt eithe ith0 be the wave operators it is known that w extend to bounded operators in l p r 4 for all 1 p if 0 is neither an eigenvalue nor a resonance of h we show that if 0 is an eigenvalue but not a resonance of h then the w are still bounded in l p r 4 for all p such that 4 3 p 4

a new construction of 16 qam near complementary sequences we present a new 16 qam near complementary sequence construction where the length of the sequences is n 2m the 16 qam near complementary sequences are constructed by nonlinear offsets but the peak to mean envelope power ratio bounds for these 16 qam near complementary sequences is as low as 2 4 the number of newly constructed 16 qam near complementary sequences is m 2 4m 1

16 qam almost complementary sequences with low pmepr a pair of sequences is said to be an almost complementary pair acp if they have zero aperiodic autocorrelation sums except at only one position over all the positive negative time shifts having correlation property very close to that of golay complementary pairs gcps acps may be used as an alternative to gcps in many applications in communications and radar for high rate code keying ofdm communication we construct novel 16 qam acps from three new classes of quadratic offsets leading to three large sets of 16 qam almost complementary sequences with maximum peak to mean envelope power ratio pmepr of 2 4

more golay sequences davis and jedwab s construction of golay sequences as reed muller codewords was believed to generate possibly all golay sequences over z sub 2 sup h of length 2 sup m from exhaustive search 1024 quaternary h 2 golay sequences of length 16 m 4 are found which are not within davis and jedwab s construction a table of 16 characteristic sequences is presented from which all 1024 golay sequences can be reconstructed the pairing information and the papr s of associated ofdm signals are given