a new class of sequences with zero or low correlation zone based on interleaving technique by interleaving one length n perfect sequence or ideal sequence according to elaborate phases a new method of construction of zero correlation zone zcz and low correlation zone lcz sequence sets is presented the resultant sequence sets are optimal or almost optimal with respect to tang fan and matsufuji bound furthermore the new method provides flexible choice for the zcz and lcz lengths

on lower bounds to the maximum correlation of complex roots of unity sequences it is shown how the welch bound 1974 on the maximum correlation of families of complex sequences of fixed norm can be modified to provide an improved bound for the case when the sequence symbols are roots of unity as in the welch bound the improved bound is based on a useful expression for the even correlation moments an analysis of the ratio of successive even moments using this expression is shown to yield a small improvement over a similarly derived bound due to v m sidelnikov 1971 interestingly the expression for the moments reduces in the binary q 2 case to a version of the pless power moment identities the derivation also provides insight into the problem of optimal sequence design

generalized binary udaya siddiqi sequences in this correspondence we present a family of binary 2n sequences of period 2 2n 1 where n is an integer which can be seen as a generalization of nonlinear binary sequences obtained from z4 sequences and recently constructed gkw gold kasami and welch like sequences the sequences have low correlations and are useful in code division multiple access cdma communication systems and cryptography

new families of binary sequences with low correlation for a positive integer n new families s and u of binary sequences of period 2 sup n 1 with low correlations are proposed where for some positive integer e s is defined for odd n e and u for even n e the family s has four valued correlations and is a generalization of the family of gold like sequences introduced by s boztas and p v kumar see ibid vol 40 p 532 7 1994 the family u which is also a generalization of the sequence family defined by p udaya polyphase and frequency hopping sequences obtained from finite rings ph d dissertation dept elec eng indian inst technol kanpur 1992 has six valued correlations the relationship between gold like sequences and gold sequences is the same as the relationship between the family s and the family constructed from the binary sequences partially contributed by r gold see ibid vol it 14 p 154 6 1968 t kasami see coordinated sci lab univ of illinois urbana champaign tech rep r 285 ad 632574 1966 and welch using a lifting idea no j s and kumar p v ibid vol 35 p 371 9 1989 for the families s and u families of binary sequences with the same correlation distributions and large linear span are also constructed

on the noncyclic property of sylvester hadamard matrices in this paper we are concerned with hadamard matrices with a certain noncyclic property first we show that when the first column of a sylvester hadamard matrix of order 2m m 2 a positive integer is removed the number of shift distinct row vectors in the matrix is given by 2m m then for m 4 we construct an infinite family of hadamard matrices with a property that when the first column of the hadamard matrix is removed all the row vectors of the matrix are shift distinct these hadamard matrices are useful in constructing low correlation zone sequences

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

on the construction of binary sequence families with low correlation and large sizes in this paper we revisit a method to produce binary sequences using the most significant bit map from z4 to the binary field this method is useful for the construction of binary sequences with low correlation and large family size there may be more cases where starting with z4 could help researchers design new low correlation sequences for code division multiple access application

heights of ideals of minors we prove new height inequalities for determinantal ideals in a regular local ring or more generally in a local ring of given embedding codimension our theorems extend and sharpen results of faltings and bruns

a geometric theory of the buchsbaum rim multiplicity abstract we develop a self contained theory of a generalized buchsbaum rim multiplicity based on elementary abstract algebraic geometry we define the multiplicity as the sum of certain natural intersection numbers and recover the traditional definition in terms of the leading coefficient of the polynomial that gives the appropriate lengths we interpret the partial sums as the multiplicities in certain closely associated cases we prove an additivity formula in the rings and relate constancy to a generalized notion of reductions we establish a polar multiplicity formula and a mixed multiplicity formula and we determine when each of the four types of multiplicities vanish we end by generalizing the height inequality for maximal minors and a celebrated theorem of boger

new design of quaternary low correlation zone sequence sets and quaternary hadamard matrices in this correspondence we present new construction methods for quaternary low correlation zone lcz sequence sets from a binary sequence with good autocorrelation we show that the sets obtained by our methods are optimal or nearly optimal with respect to the tang fan matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period family size and zone size we also give a construction method for a quaternary lcz sequence set from a binary lcz sequence set finally we give a new construction method for quaternary hadamard matrices by the inverse of the gray map

generalized kasami sequences the large set in this correspondence new binary sequence families fk of period 2n 1 are constructed for even n and any k with gcd k n 2 if n 2 is odd or gcd k n 1 if n 2 is even the distribution of their correlation values is completely determined these families have maximum correlation 2n 2 1 and family size 23n 2 2n 2 for odd n 2 or 23n 2 2n 2 1 for even n 2 the proposed families include the large set of kasami sequences where the k is taken as k n 2 1

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

mixed buchsbaum rim multiplicities we prove the results about mixed buchsbaum rim multiplicities announced in 6 9 10 ii p 224 including a general mixed multiplicity formula in addition we identify these multiplicities as the coefficients of the leading form of the appropriate buchsbaum rim polyno mial in three variables and we prove a positivity theorem in fact we define the multiplicities as the degrees of certain zero dimensional mixed twisted segre classes and we develop an encom passing general theory of these new rational equivalence classes in all dimensions in parallel we develop a theory of pure twisted segre classes and we recover the main results in 6 about the pure buchsbaum rim multiplicities the polar multiplicities and so forth moreover we identify the additivity theorem 6 6 7b i p 205 as giving a sort of residual intersection formula and we show its somewhat unexpected connection to the mixed multiplicity formula also we work in a more general setup than in 6 and we develop a new approach based on the completed normal cone 1 introduction the theory of mixed multiplicities of primary ideals was introduced by teissier in his study of complex hypersurface germs with isolated singularities a decade later gaffney began extending teissier s work to com plete intersections and was led to conjecture a theory of generalized multiplicities of submodules of finite colength in a free module including an important mixed multiplicity formula for the product of an ideal and a submodule it turned out that these generalized multiplicities are nothing but the multiplicities introduced a decade before teissier s work by buchsbaum and rim who established many of their fundamental properties but no mixed multiplicity formula recently the authors gave a general treatment of the buchsbaum rim multiplicity based on blowups and intersection numbers in 6 that paper also contains a more exten sive history of the subject on p 225 the authors announced a mixed multiplicity formula for an arbitrary pair of submodules here we prove an even more general formula and show that it s closely related surprisingly to another fundamental formula the additivity formula we also simplify generalize and advance the previous treatment via a new approach sections 2 and 3 study two preliminary notions module transforms and dis tinguished subsets section 4 studies a twisted version ofthe usual segre classes of a subscheme the degrees of these classes yield the buchsbaum rim multi plicities moreover the usual theory of segre classes leads to simpler and more

formulas for the multiplicity of graded algebras let r be a standard graded noetherian algebra over an artinian local ring moti vated by the work of achilles and manaresi in intersection theory we first express the multiplicity of r by means of local j multiplicities of various hyperplane sections when applied to a homogeneous inclusion ab of standard graded noetherian algebras over an artinian local ring this formula yields the multiplicity of a in terms of that of b and of local j multiplicities of hyperplane sections along proj b our formulas can be used to find the multiplicity of special fiber rings and to obtain the degree of dual va rieties for any hypersurface in particular it gives a generalization of teissier s plucker formula to hypersurfaces with non isolated singularities our work generalizes results by simis ulrich and vasconcelos on homogeneous embeddings of graded algebras

a new binary sequence family with low correlation and large size for odd n 2l 1 and an integer spl rho with 1 spl les spl rho spl les l a new family s sub o spl rho of binary sequences of period 2 sup n 1 is constructed for a given spl rho s sub o spl rho has maximum correlation 1 2 sup n 2 spl rho 1 2 family size 2 sup n spl rho and maximum linear span n n 1 2 similarly a new family of s sub e spl rho of binary sequences of period 2 sup n 1 is also presented for even n 2l and an integer spl rho with 1 spl les spl rho l where maximum correlation family size and maximum linear span are 1 2 sup n 2 spl rho 2 sup n spl rho and n n 1 2 respectively the new family s sub o spl rho or s sub e spl rho contains boztas and kumar s construction or udaya s as a subset if m sequences are excluded from both constructions as a good candidate with low correlation and large family size the family s sub o 2 is discussed in detail by analyzing its distribution of correlation values

new families of codebooks achieving the levenstein bound in this paper a construction of codebooks based on a set of bent functions satisfying certain conditions is introduced it includes some earlier constructions of codebooks meeting the levenstein bound as special cases with this construction two new families of codebooks achieving the levenstein bound are obtained the codebooks constructed in this paper could have a very small alphabet size

priors and likelihoods that are arbitrarily sensitive to outlying observations summary for location parameters the posterior can be extremely sensitive to the functional forms of the prior and likelihood when there is an extreme outlying observation conditions on the prior likelihood and set are provided such that as one observation goes to infinity the posterior probability that a location parameter is contained in the set goes to zero this is of particular interest when the set ranges over intervals with a finite upper bound the conditions for this extreme reaction to an outlying observation cover all box tiao densities with a shape parameter greater than one

on quadratic bent functions in polynomial forms in this correspondence we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields the results improve some previous work moreover we solve a problem left by yu and gong in 2006

binary almost perfect sequence sets sequence set with lower correlation values is highly desired for engineering applications however theoretical results e g welch bound show that max n in general that is the maximum out of phase autocorrelation and cross correlation magnitudes of a sequence set is not less than the square root of the sequence period in this paper we propose a new concept namely almost perfect sequence set apss which has the property max c except for at most m shifts where c and m are predefined small integers a uniform method is presented to construct apss and then the properties of such apss are discussed moreover a distance inequality on the apss with m 1 is obtained and several apss families such as 2p 8p 2 6 4 apss and 3p 64p2 8 3 9 9 apss for any prime p 5 are constructed based on paley and paley partial sequences finally it shows that the apss can be used to construct lcz sequences and the properties of such lcz sequences are presented

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

multiplicative characters the weil bound and polyphase sequence families with low correlation power residue and sidelnikov sequences are polyphase sequences with low correlation and variable alphabet sizes represented by multiplicative characters in this paper sequence families constructed from the shift and addition of the polyphase sequences are revisited initially 0 1 is assumed for multiplicative characters to represent power residue and sidelnikov sequences in a simple form the weil bound on multiplicative character sums is refined for the assumption where the character sums are equivalent to the correlations of sequences represented by multiplicative characters general constructions of polyphase sequence families that produce some of known families as the special cases are then presented the refined weil bound enables the efficient proofs on the maximum correlation magnitudes of the sequence families from the constructions it is shown that m ary known sequence families with large size can be partitioned into m 1 disjoint subsequence families with smaller maximum correlation magnitudes more generalized constructions are also considered by the addition of multiple cyclic shifts of power residue and sidelnikov sequences

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

when is conflict normal abstract when data conflicts with quantified prior beliefs seemingly small changes in the functional form of the prior and or likelihood can have a profound effect on posterior inferences this article provides results on asymptotic forms of the posterior when two information sources conflict in particular let x be from the likelihood p 2 x with an unknown location parameter with p 1 the prior on sufficient conditions on p 1 and p 2 are provided to ensure that as x the posterior is asymptotically normal the conditions cover all combinations in which p 1 and p 2 are proportional to exp x i i with i 1 conditions are also provided that ensure that as some of the data become extreme the posterior variance goes to 0 converges to a constant or diverges to infinity other asymptotic behavior involving conflicting information sources is also discussed

a new family of p ary sequences with low correlation constructed from decimated sequences in this paper for an odd prime p and an integer n geq 3 a new family of p ary sequences of period p n 1 over 2 with low correlation is constructed the new family is constructed by shifts and additions of two decimated sequences of a p ary m sequence and its family size is 2 p n 1 the complete correlation distribution of this new family is derived it is also shown that the family is optimal with respect to the parameter theta rm rms which denotes the root mean square of all nontrivial correlations compared with the known sequence families our sequence family is new and has a larger family size which is four times of its period

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

new construction for families of binary sequences with optimal correlation properties we present a construction in a closed form for an optimal family of 2 sup m binary sequences of period 2 sup 2m 1 with respect to welch s 1974 bound whenever there exists a balanced binary sequence of period 2 sup m 1 with ideal autocorrelation property using the trace function this construction enables us to reinterpret a small set of kasami and no 1988 sequences as a family constructed from m sequences new optimal families of binary sequences are constructed from the legendre sequences of mersenne prime period hall s sextic residue sequences and miscellaneous sequences of unknown type in addition we enumerate the number of distinct families of binary sequences which are constructed from a given binary sequence by this method

gmw sequences corresp the difference set design of gordon mills and welch gmw is adapted for use as a pseudorandom number generator statistical properties of the generated binary sequences including periodic correlation linear span and k tuple statistics are derived one mechanization of a gmw sequence generator is suggested and the number of sequences that can be generated with a fixed number of shift register stages and read only memory rom size is evaluated

constructions of quadratic bent functions in polynomial forms in this correspondence the constructions and enumerations of all bent functions represented by a polynomial form of f x spl sigma sub i 1 sup n 2 1 c sub i tr x sup 1 2 i c sub n 2 tr sub 1 sup n sup 2 x sup 1 2 n 2 c sub i spl isin sub 2 f sub 2 are presented for special cases of n using an iterative approach the construction of bent functions of n variables with degree n 2 is also provided using the constructed quadratic bent functions

a new family of nonbinary sequences with three level correlation property and large linear span in this correspondence we present a new family of nonbinary sequences with three level nontrivial correlations and large linear complexity the sequences may be considered as nonlinear analogues of the well known sequences by trachtenberg and helleseth it is shown that the family is optimal with respect to the welch bound in terms of root mean square of all nontrivial correlations we also determine the correlation distribution of the new family

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

posterior bimodality in the balanced one way random effects model summary although some researchers have examined posterior multimodality for specific richly parameterized models multimodality is not well characterized for any such model the paper characterizes bimodality of the joint and marginal posteriors for a conjugate analysis of the balanced one way random effects model with a flat prior on the mean this apparently simple model has surprisingly complex and even bizarre mode behaviour bimodality usually arises when the data indicate a much larger between groups variance than does the prior we examine an example in detail present a graphical display for describing bimodality and use real data sets from a statistical practice to shed light on the practical relevance of bimodality for these models

multiplicities of classical varieties the j multiplicity plays an important role in the intersec tion theory of stuckrad vogel cycles while recent developments confirm the connections between the e multiplicity and equisingularity theory in this paper we establish under some constraints a relation ship between the j multiplicity of an ideal and the degree of its fiber cone as a conse quence we are able to compute the j multiplicity of all the ideals defin ing rational normal scrolls by using the standard monomial theory we can also compute the j and e multiplicity of ideals defining determinan tal varieties the found quantities are integrals which qu ite surprisingly are central in random matrix theory

linkage and the koszul homology of ideals 0 introduction let r be a local ring and i an ideal of r associated to i are several graded algebras the symmetric algebra of the module i sym i the rees algebra of i defined to be the algebra r i gn o inf and the associated graded algebra of i gr1 r rii g ii 2 in in 1 i i i our purpose in this paper is to study the behavior of these graded algebras when we change i through linkage recall the definition of linkage found in the paper of peskine and szpiro 22

new sets of zero or low correlation zone sequences via interleaving techniques sequence families with zero or low correlation zone can be used in the quasi synchronous code division multiple access qs cdma communication systems interleaving techniques are very useful for sequence design in this paper we present a general construction of sequence families with zero or low correlation zone using interleaving techniques and complex hadamard matrices the component sequences are perfect or ideal two level in two cases we construct the shift sequences 1 p l 2 p is even and l p 2 mod p which results in sequence families with zero or low correlation zone of parameters np mp l p where n is the period of component sequences m is the number of inequivalent shift sequences and 0 or 1 the conditions are derived under which the new construction is optimal some examples are also given to specify the new construction

bounds on the linear span of bent sequences recently olsen scholtz and welch presented families of binary sequences called bent function sequences which can be generated through nonlinear operations on m sequences these families of sequences possess asymptotically optimum correlation properties and large equivalent linear span els upper and lower bounds to the els of bent function sequences are derived the upper bound improves upon key s upper bound and the lower bound obtained through construction and exceeds left stackrel n 2 n 4 right cdot 2 n 4 where n is the length of the shift register generating the m sequence an interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose els is guaranteed to be large

generalized hilbert coefficients and northcott s inequality abstract let r be a cohen macaulay local ring of dimension d with infinite residue field let i be an r ideal that has analytic spread l i d satisfies the g d condition and the weak artin nagata property a n d 2 we provide a formula relating the length i n 1 j i n to the difference p i n h i n where j is a general minimal reduction of i p i n and h i n are respectively the generalized hilbert samuel polynomial and the generalized hilbert samuel function we then use it to establish formulas to compute the generalized hilbert coefficients of i as an application we extend northcott s inequality to non m primary ideals furthermore when equality holds we prove that the ideal i enjoys nice properties indeed if this is the case then the reduction number of i is at most one and the associated graded ring of i is cohen macaulay we also recover results of g colome nin c polini b ulrich and y xie on the positivity of the generalized first hilbert coefficient j 1 i our work extends that of s huckaba c huneke and a ooishi to ideals that are not necessarily m primary

bent and hyper bent functions in polynomial form and their link with some exponential sums and dickson polynomials bent functions are maximally nonlinear boolean functions with an even number of variables they were introduced by rothaus in 1976 for their own sake as interesting combinatorial objects but also because of their relations to coding theory reed muller codes and applications in cryptography design of stream ciphers they have attracted a lot of research specially in the last 15 years the class of bent functions contains a subclass of functions introduced by youssef and gong in 2001 the so called hyper bent functions whose properties are still stronger and whose elements are still rarer than bent functions bent and hyper bent functions are not classified a complete classification of these functions is elusive and looks hopeless so it is important to design constructions in order to know as many of hyper bent functions as possible this paper is devoted to the constructions of bent and hyper bent boolean functions in polynomial forms we survey and present an overview of the constructions discovered recently we extensively investigate the link between the bentness property of such functions and some exponential sums involving dickson polynomials and give some conjectures that lead to constructions of new hyper bent functions

koszul modules and gorenstein algebras abstract i first define koszul modules which are a generalization to arbitrary rank of complete intersections after a study of some of their properties it is proved that gorenstein algebras of codimension one or two over a local or graded cm ring are koszul modules thus generalizing a well known statement for rank one modules the general techniques used to describe koszul modules are then used to obtain a structure theorem for gorenstein algebras in codimension one and two over a local or graded cm ring

optimal codebooks from binary codes meeting the levenshtein bound in this paper a generic construction of codebooks based on binary codes is introduced with this generic construction a few previous constructions of optimal codebooks are extended and a new class of codebooks almost meeting the levenshtein bound is presented exponentially many codebooks meeting or almost meeting the levenshtein bound from binary codes are obtained in this paper the codebooks constructed in this paper have alphabet size 4 as a byproduct three bounds on the parameters of binary codes are derived

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

new constructions of quaternary low correlation zone sequences in this paper given a composite integer n we propose a method of constructing quaternary low correlation zone lcz sequences of period 2 sup n 1 from binary sequences of the same length with ideal autocorrelation these new sequences are optimal with respect to the bound by tang fan and matsufuji the correlation distributions of these new quaternary lcz sequences constructed from m sequences and gordon mills welch gmw sequences are derived

binary sequence sets with favorable correlations from difference sets and mds codes we propose new families of pseudorandom binary sequences based on hadamard difference sets and mds codes we obtain for p 4k 1 prime and t an integer with 1 spl les t spl les p 1 2 a set of p sup t binary sequences of period p sup 2 whose peak correlation is bounded by 1 2t p 1 the sequences are balanced have high linear complexity and are easily generated

mixed multiplicities segre numbers and segre classes abstract based on classical results of rees and on multivariate hilbert polynomials we define new mixed multiplicities of two arbitrary ideals in a local ring a m and use them to express the local degrees of all varieties appearing in the gaffney gassler construction of segre cycles we prove that the classical mixed multiplicities of m and an arbitrary ideal i which are a special case of the new ones are equal to the generalized samuel multiplicities of an ideal in the rees algebra r i a this equality is used to improve a result of jeffries montano and varbaro on the degree of the fiber cone of an ideal we conclude the paper with formulas and their inverses which express the degrees of segre classes of subschemes of arbitrary projective varieties by generalized samuel multiplicities or by classical mixed multiplicities using the mixed multiplicities of balanced rational normal scrolls which have been computed by hoang and lam we find the mixed multiplicities of all rational normal scrolls as well as their segre classes and their generalized samuel multiplicities

global representation of segre numbers by monge ampere products on a reduced analytic space x we introduce the concept of a generalized cycle which extends the notion of a formal sum of analytic subspaces to include also a form part we then consider a suitable equivalence relation and corresponding quotient mathcal b x that we think of as an analogue of the chow group and a refinement of de rham cohomology this group allows us to study both global and local intersection theoretic properties we provide many mathcal b analogues of classical intersection theoretic constructions for an analytic subspace v subset x we define a mathcal b segre class which is an element of mathcal b x with support in v it satisfies a global king formula and in particular its multiplicities at each point coincide with the segre numbers of v when v is cut out by a section of a vector bundle we interpret this class as a monge ampere type product for regular embeddings we construct a mathcal b analogue of the gysin morphism

on the correlation distributions of the optimal quaternary sequence family cal u and the optimal binary sequence family cal v recently new optimal families s and u of quaternary sequences have been presented and the optimal binary sequence family v obtained from family s under gray map has been investigated as well the two sequence families u and v are optimal with respect to the well known sidelnikov bound and welch bound but their exact correlation distributions are not known until now in this paper their exact correlation distributions are completely determined in some cases by making use of exponential sums and the theory of z4 valued quadratic forms

koszul homology and the structure of low codimension cohen macaulay ideals the relationship between the properties of the koszul homology modules of two ideals connected by linkage is studied if the ideal i is either i a cohen macaulay ideal of codimension 3 or ii a gorenstein ideal of codimension 4 the one dimensional koszul module carries considerable information on the struct ural nature of the linkage class of i in case i or on the conormal module of i in case ii emphasis is given to the verification of the properties by computation introduction the aim of this paper is to examine the structure of cohen macaulay ideals of low i e 3 and 4 codimension as it is expressed by the koszul homology modules more specifically given a perfect ideal i of a gorenstein nng r we are interested in how i its numerical data e g betti numbers and degrees of its generating syzygies in the case of a homogeneous ideal ii properties of the full linkage class of i and iii whether i is suitably generated e g generated by a d sequence are mirrored on the module and the algebra structures of the homology of the koszul complex build on a generating set of i the man result theorem 2 4 is the proof that for a perfect ideal i of codimension threes the condition that the 1 dimensional koszul homology module h1 i r be cohen macaulay is an invanant of the full linkage class of i the framework for this result is provided by several facts first the classical descnptions of cohen macaulay ideals of codimension two and of gorenstein ideals of heit ht three as belonging to the linkage classes of complete intersections a be ga w then a theorem of huneke hu1 asserting that the property hi i r is cohen macaulay for i ms is an invariant of the eren linkage class of i finally in case of ideals of polynomial rings data on the koszul homology has the advantage of being in principle known at the outset that is hypotheses on them can be venfied once the ideal has been specified by a set of generators in the last section we indicate how symbolic computation packages may be used to obtain this informa tion to contrast already in the case of codimension four gorenstein ideals the depths of the koszul homology modules of directly linked ideals may differ sharply furthermore in codimension three we show that this invanance does not extend to the next koszul module to further enhance the role of h1 i r as a carrier of

on a conjectured ideal autocorrelation sequence and a related triple error correcting cyclic code in a previous paper no golomb gong lee and gaal see ibid vol 44 p 814 17 1998 conjectured that certain binary sequences having a simple trace description possess the ideal autocorrelation property in the present paper it is shown that each such sequence is balanced and moreover that the dual of the linear cyclic code generated by the sequence and its cyclic shifts is a triple error correcting code having the same weight distribution as the triple error correcting bose chaudhuri hocquenghem bch code this cyclic code also contains a cyclic subcode that yields a new family of sequences having the same size and correlation parameters as does the family of gold sequences

two new families of optimal binary sequences obtained from quaternary sequences in this paper we present two optimal binary families of sequences of length 2n 1 and 2 2n 1 for odd integer n they are obtained as the images of proposed optimal quaternary sequences under the most significant bit and the gray maps the first family has 2n 1 sequences of length 2n 1 and the identical correlation distribution to that of gold sequences and gold like sequences and the second family of sequences of length 2 2n 1 has 2n sequences and the same correlation values as those of kerdock sequences

a generalization of the family of p ary decimated sequences with low correlation let p be a prime and n a positive integer let e pn 1 and n pn 1 e in this paper we construct a family s of e2n p ary sequences each member of s has period n and the magnitudes of correlations of members of s are upper bounded by 2 pn 2 en 1

strongly cohen macaulay schemes and residual intersections this paper studies the local properties of closed subschemes y in cohen macaulay schemes x such that locally the defining ideal of y in x has the property that its koszul homology is cohen macaulay whenever this occurs y is said to be strongly cohen macaulay in x this paper proves several facts about such embeddings chiefly with reference to the residual intersections of y in x the main result states that any residual intersection of y in x is again cohen macaulay introduction our purpose in this paper is to investigate a property of a closed subscheme y in a noetherian cohen macaulay scheme x which we call strong cohen macaulayness this is a local property which we first describe for a local ring let x spec r where r is a cohen macaulay local ring and let y spec r i

new optimal quadriphase sequences with larger linear span in this paper two new optimal families s and u of quadriphase sequences are presented compared to the family a constructed by boztas and the family d investigated by tang respectively the proposed families have the same optimal correlation properties and family size but larger linear spans

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

generic construction of quaternary sequences of period 2n with low correlation from quaternary sequences of odd period n in this paper a simple but generic method is proposed for transforming any family of quaternary sequences with low correlation of any odd period n to another family of quaternary sequences of period 2n with low correlation as an application of the generic method to sequence family a a new optimal quaternary sequence family with length 2 2n 1 family size 2n 1 and maximal nontrivial correlation value 2 n 1 2 2 where n is an odd integer is obtained most notably unlike all the known optimal quaternary sequence families the new family has a unique property that the odd integers 1 3 and the even integers 0 2 are allocated alternatively in all the sequences

multiplicity sequence and integral dependence we prove that two arbitrary ideals i subset j in an equidimensional and universally catenary noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence we also obtain a principle of specialization of integral dependence which gives a condition for integral dependence in terms of the constancy of the multiplicity sequence in families

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

the decimation hadamard transform of two level autocorrelation sequences a new method to study and search for two level autocorrelation sequences for both binary and nonbinary cases is developed this method iteratively applies two operations decimation and the hadamard transform based on general orthogonal functions referred to as the decimation hadamard transform dht the second iterative dht can transform one class of such sequences into another inequivalent class of such sequences a process called realization the existence and counting problems of the second iterative dht are discussed using the second iterative dht and starting with a single binary m sequence when n is odd we believe one can obtain all the known two level autocorrelation sequences of period 2 sup n 1 which have no subfield factorization we have verified this for odd n spl les 17 interestingly no previously unknown examples were found by this process for any odd n spl les 17 this is supporting evidence albeit weak for the conjecture that all families of cyclic hadamard difference sets of period 2 sup n 1 having no subfield factorization are now known at least for odd n experimental results are provided

a note on low correlation zone signal sets in this correspondence we present a connection between designing low correlation zone lcz sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors this results in lcz signal sets with huge sizes over three different alphabetic sets finite field of size integer residue ring modulo and the subset in the complex field which consists of powers of a primitive th root of unity we show a connection between these sequence designs and ldquocompletely noncyclicrdquo hadamard matrices and a construction for those sequences we also provide some open problems along this direction

explicit full correlation distribution of sequence families using plateaued functions the design of code division multiple access sequence families dates back to the gold sequences from the 1960s since then there has been a number of different such designs with good correlation properties some optimal and some near optimal in this paper we use the concept of plateaued functions with arbitrary degree in order to compute their full correlation distributions first we give an explicit correlation distribution of a sequence family using a non quadratic function then for the quadratic functions we present a general classification of gold like sequence families for all possible characteristics p and degrees n of the galois field mathbb f p n used to define the sequences we are able to obtain the full correlation distribution of the families we consider this paper also uses techniques from the theory of algebraic curves in order to obtain some of the results

segre numbers a generalized king formula and local intersections let mathcal j be an ideal sheaf on a reduced analytic space x with zero set z we show that the lelong numbers of the restrictions to z of certain generalized monge ampere products dd c log f 2 k where f is a tuple of generators of mathcal j coincide with the so called segre numbers of mathcal j introduced independently by tworzewski achilles manaresi and gaffney gassler more generally we show that these currents satisfy a generalization of the classical king formula that takes into account fixed and moving components of vogel cycles associated with mathcal j a basic tool is a new calculus for products of positive currents of bochner martinelli type we also discuss connections to intersection theory

explicit criteria for construction of plateaued functions plateaued functions are very important cryptographic functions due to their desirable cryptographic characteristics we find explicit criteria for the construction of p ary r plateaued functions with an odd prime p we point out that 0 plateaued functions are bent functions and so plateaued functions generalize the notion of bent functions we first derive an explicit form for the walsh hadamard transform of a p ary r plateaued function we then obtain an upper bound on the degree of p ary r plateaued functions and we classify p ary n 1 plateaued functions in n variables we also obtain explicit criteria for the existence of p ary r plateaued functions accordingly these results lead to improved bounds on the existence of p ary bent functions