injectivity of compressing maps on primitive sequences over bbz p e let zopf pe be the integer residue ring with odd prime p and integer eges2 for a sequence a over zopf pe one has a unique p adic expansion a a 0 a 1 p a e 1 pe 1 where a i can be regarded as a sequence over zopf p for 0lesilese 1 let f x be a strongly primitive polynomial over zopf pe and g f x pe be the set of all primitive sequences generated f x by over zopf pe recently the authors xuan yong zhu and wen feng qi have proved that for a function phi x0 xe 1 g xe 1 eta x0 xe 2 over zopf p and a b ising f x pe where 2lesdeg glesp 1 phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b to further complete their work we show that such injectivity also holds for deg g 1 that is for a function phi x0 xe 1 xe 1 eta x0 xe 2 over zopf p and a b ising f x pe phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b

a 2 adic approach to the analysis of cyclic codes this paper describes how 2 adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over z sub 2 a a spl ges 2 the ring of integers modulo 2 sup a it provides a 2 adic proof of a theorem of mceliece that characterizes the possible hamming weights that can appear in a binary cyclic code a generalization of this theorem is derived that applies to cyclic codes over z sub 2 a that are obtained from binary cyclic codes by a sequence of hensel lifts this generalization characterizes the number of times a residue modulo 2 sup a appears as a component of an arbitrary codeword in the cyclic code the limit of the sequence of hensel lifts is a universal code defined over the 2 adic integers this code was first introduced by calderbank and sloane 1995 and is the main subject of this paper binary cyclic codes and cyclic codes over z sub 2 a are obtained from these universal codes by reduction modulo some power of 2 a special case of particular interest is cyclic codes over z sub 4 that are obtained from binary cyclic codes by means of a single hensel lift the binary images of such codes under the gray isometry include the kerdock preparata and delsart goethals codes these are nonlinear binary codes that contain more codewords than any linear code presently known fundamental understanding of the composition of codewords in cyclic codes over z sub 4 is central to the search for more families of optimal codes this paper also constructs even unimodular lattices from the hensel lift of extended binary cyclic codes that are self dual with all hamming weights divisible by 4 the leech lattice arises in this way as do extremal lattices in dimensions 32 through 48

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

the koch monopole a small fractal antenna fractal objects have some unique geometrical properties one of them is the possibility to enclose in a finite area an infinitely long curve the resulting curve is highly convoluted being nowhere differentiable one such curve is the koch curve in this paper the behavior the koch monopole is numerically and experimentally analyzed the results show that as the number of iterations on the small fractal koch monopole are increased the q of the antenna approaches the fundamental limit for small antennas

quadriphase sequences for spread spectrum multiple access communication this paper studies constructions for quadriphase sequences that are suitable for use as signature sequences in quadriphase spread spectrum multiple access communications quadriphase sequences are closely related to biphase i e binary sequences and many of the properties of the former can be expressed in terms of properties of the latter methods of construction are presented which obtain sets of quadriphase sequences from sets of biphase sequences methods of construction of quadriphase sequences are provided based upon the properties of the multiplicative characters of the finite field gf q where q equiv 1 mod 4 these methods use codewords from low rate reed solomon codes which are mapped onto the fourth roots of unity 2q 2 sequences of period q 1 are constructed for which the maximum magnitudes of the periodic cross correlation and the periodic out of phase autocorrelation are bounded by 3 sqrt q 5

the gauss green theorem for fractal boundaries v is the 1 vectorfield dual to if 1 fi dx1 dxi dxn then v f1 fn there has been considerable effort in the literature e g jk m p to extend this formula to permit integrands of less regularity by generalizing the lebesgue integral on the other hand invariably the situations in which 1 holds require fairly strong hypotheses on the boundary e g that it should have sigmafinite n 1 measure or that the gradient of the characteristic function of be a vector valued measure with finite total variation f p however there is a natural way to expand the validity of 1 to much more general boundaries while still using the ordinary lebesgue integral this is the topic of the present paper for the case of lipschitz forms the results of this paper follow readily from whitney s theory of flat chains w2 however his approach to the gauss green theorem is not widely appreciated because he focused on chains and cochains where effectively 1 is used to define the exterior derivative in hn we extend whitney s method to treat the more general holder case only the case n 2 is discussed

the stiffness of self similar fractals abstract a method to derive the stiffness of self similar elastic fractals is presented based on structural mechanics principles and a physically motivated similarity criterion which is assumed as a postulate using this method the stiffnesses of both the von koch curve and the sierpinski gasket in the small deformation regime are derived for these fractal structures it is shown that the stiffness matrix is completely determined by a single elastic constant the procedure to tile a planar domain with sierpinski gaskets is explored and shown to require the consideration of hexagonal shaped combinations of gaskets joined continuously along their edges this continuity leads to a phenomenon of geometrically induced inextensibility along the common edges after deriving the stiffness matrix for the basic hexagon the analog of the boussinesq flamant problem for a tiled half plane is solved numerically to demonstrate the potential of the method in modeling of solid mechanics applications

anisotropic fractal media by vector calculus in non integer dimensional space a review of different approaches to describe anisotropic fractal media is proposed in this paper differentiation and integration non integer dimensional and multi fractional spaces are considered as tools to describe anisotropic fractal materials and media we suggest a generalization of vector calculus for non integer dimensional space by using a product measure method the product of fractional and non integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models the integration over non integer dimensional spaces is considered in this paper differential operators of first and second orders for fractional space and non integer dimensional space are suggested the differential operators are defined as inverse operations to integration in spaces with non integer dimensions non integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media the poisson s equation for fractal medium the euler bernoulli fractal beam and the timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media

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 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

local fractional fokker planck equation we propose a new class of differential equations which we call local fractional differential equations they involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time a local fractional analog of the fokker planck equation has been derived starting from the chapman kolmogorov condition we solve the equation with a specific choice of the transition probability and show how subdiffusive behavior can arise

free vibration analysis of a von koch beam in this paper the free undamped motion of a cantilever von koch beam is investigated the reduction of the stiffness and mass matrices leads to simple analytical recursive relationships depending on the fractal dimension of the structure results are then extended to perform a detailed modal analysis which suggests peculiar scaling laws for the natural frequencies and modal shapes of the structure energy considerations are also provided finally the potentiality of the von koch beam as a fractal antenna is examined in terms of resonant frequencies

bbz _4 valued quadratic forms and quaternary sequence families in this paper zopf4 valued quadratic forms defined on a vector space over gf 2 are studied a classification of such forms is established distinguishing zopf4 valued quadratic forms only by their rank and whether the associated bilinear form is alternating this result is used to compute the distribution of certain exponential sums which occur frequently in the analysis of quaternary codes and quaternary sequence sets the concept is applied as follows when t 0 or m is odd the correlation distribution of family s t consisting of quaternary sequences of length 2 m 1 is established then motivated by practical considerations a subset s t of family s t is defined and the correlation distribution of family s t is given for odd and even m

long range cohesive interactions of non local continuum faced by fractional calculus abstract a non local continuum model including long range forces between non adjacent volume elements has been studied in this paper the proposed continuum model has been obtained as limit case of two fully equivalent mechanical models i a volume element model including contact forces between adjacent volumes as well as long range interactions distance decaying between non adjacent elements ii a discrete point spring model with local springs between adjacent points and non local springs with distance decaying stiffness connecting non adjacent points under the assumption of fractional distance decaying interactions between non adjacent elements a fractional differential equation involving marchaud type fractional derivatives has been obtained for unbounded domains it is shown that for unbounded domains the two mechanical models revert to lazopoulos and eringen model with fractional distance decaying functions it has also been shown that for a confined bar the stress strain relation is substantially different from that obtained simply using the truncated marchaud derivatives since a double integral instead of convolution integral appears moreover in the analysis of bounded domains the governing equations turn out to an integro differential equation including only the integral part of marchaud fractional derivatives on finite interval the mechanical boundary condition for the proposed model has been introduced consistently on the basis of mechanical considerations and the constitutive law of the proposed continuum model has been reported by mathematical induction several numerical applications have been reported to show verify and assess the concepts listed in this paper

phase transitions for countable markov shifts we study the analyticity of the topological pressure for some one parameter families of potentials on countable markov shifts we relate the non analyticity of the pressure to changes in the recurrence properties of the system we give sufficient conditions for such changes to exist and not to exist we apply these results to the manneville pomeau map and use them to construct examples with different critical behavior

scaling laws and renormalization groups for strength and toughness of disordered materials abstract the abundant literature on tensile strength and fracture energy size effects as well as the newly introduced fractal and renormalization group theories would appear to indicate the need for a dramatic change in our conceptual framework if we want to consider and measure material constants in strength of materials as well as in fracture mechanics for disordered materials such as for example concrete and rocks the renormalized tensile strength is given by a force acting on a surface having a fractal dimension lower than 2 just as the renormalized fracture energy is represented by a dissipation over a surface with a dimension higher than 2 in the case of tensile strength the dimensional decrement represents self similar weakening of the reacting cross section or ligament due to pores voids defects cracks aggregates inclusions etc likewise in the case of fracture energy the dimensional increment represents self similar tortuosity of the fracture surface due to aggregates and inclusions as well as self similar microcrack overlapping and distribution also in the direction orthogonal to that of the forming macrocrack it can be demonstrated that the sum of the dimensional decrement for material ligament and the dimensional increment for fracture surface must be lower than unity

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

on the odd and the aperiodic correlation properties of the kasami sequences derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small kasami family the approach is based on a technique described in s litsyn and a tietavainen 1994 that is originally due to i m vinogradov 1954 an essential ingredient in this method is a good upper bound on the discrete fourier coefficients of a shifted product of a pair of sequences the author obtains an upper bound of the order o spl radic llnl for the maximal aperiodic and odd correlation magnitudes for sequences of length l

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

the most significant bit of maximum length sequences over spl zopf 2 sup l autocorrelation and imbalance the imbalance and the autocorrelation of the binary sequences in the title are explored by combining the local weil bound with spectral analysis recent estimates on these quantities are improved by a factor of order 2 sup l 2 for large l

optimal biphase sequences with large linear complexity derived from sequences over z sub 4 new families of biphase sequences of size 2 sup r 1 1 r being a positive integer are derived from families of interleaved maximal length sequences over z sub 4 of period 2 2 sup r 1 these sequences have applications in code division spread spectrum multiuser communication systems the families satisfy the sidelnikov bound with equality on spl theta sub max which denotes the maximum magnitude of the periodic cross correlation and out of phase autocorrelation values one of the families satisfies the welch bound on spl theta sub max with equality the linear complexity and the period of all sequences are equal to r r 3 2 and 2 2 sup r 1 respectively with an exception of the single m sequence which has linear complexity r and period 2 sup r 1 sequence imbalance and correlation distributions are also computed

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 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

p adic valuation of weights in abelian codes over spl zopf p sup d counting polynomial techniques introduced by wilson are used to provide analogs of a theorem of mceliece mceliece s original theorem relates the greatest power of p dividing the hamming weights of words in cyclic codes over gf p to the length of the smallest unity product sequence of nonzeroes of the code calderbank li and poonen presented analogs for cyclic codes over zopf 2d using various weight functions hamming lee and euclidean weight as well as count of occurrences of a particular symbol some of these results were strengthened by wilson who also considered the alphabet zopf pd for p an arbitrary prime these previous results new strengthened versions and generalizations are proved here in a unified and comprehensive fashion for the larger class of abelian codes over zopf pd with p any prime for abelian codes over zopf 4 combinatorial methods for use with counting polynomials are developed these show that the analogs of mceliece s theorem obtained by wilson for hamming weight lee weight and symbol counts and the analog obtained here for euclidean weight are sharp in the sense that they give the maximum power of 2 that divides the weights of all the codewords whose fourier transforms have a specified support

on the relationship between fractal dimension and the performance of multi resonant dipole antennas using koch curves this paper relates for the first time multiple resonant frequencies of fractal element antennas using koch curves to their fractal dimension dipole and monopole antennas based fractal koch curves studied so far have generally been limited to certain standard configurations of the geometry it is possible to generalize the geometry by changing its indentation angle to vary its fractal similarity dimension this variation results in self similar geometry which can be generated by a recursive algorithm such a variation is found to have a direct influence on the input characteristics of dipole antennas the primary resonant frequency the input resistance at this resonance and the ratio of first two resonant frequencies have all been directly related to the fractal dimension curve fit expressions can also be obtained for the performance of antennas at their primary resonance in terms of fractal iteration and fractal dimension the antenna characteristics have been studied using extensive numerical simulations and are experimentally verified these findings underscore the significance of fractal dimension as an important mathematical property of fractals that can be used as a design parameter for antennas the use of these ideas would not only reduce the computational intensity of optimization approaches for design of fractal shaped antennas but also help antenna designers approach the problem systematically design formulation for antennas based on other fractal geometries can be similarly obtained after identifying suitable parameters of variation this would therefore help analytical design of multiband and multifunctional antennas using fractal geometries

on the behavior of koch island fractal boundary microstrip patch antenna the properties of the koch island fractal boundary microstrip patch antenna are presented the behavior at the fundamental mode and the existence of high order modes that exhibit localized current density distributions is discussed the main features are the size reduction of the patch resonating at the fundamental frequency when compared to euclidean shaped patches and the application of localized modes in designing microstrip patch antennas with directive patterns

incomplete exponential sums over galois rings with applications to some binary sequences derived from z sub 2 sup l an upper bound for the incomplete exponential sums over galois rings is derived explicitly based on the incomplete exponential sums we analyze the partial period properties of some binary sequences derived from z sub 2 sup l in detail such as the kerdock code binary sequences and the highest level sequences of primitive sequences over z sub 2 sup l the results show that the partial period distributions and the partial period independent r pattern distributions of these binary sequences are asymptotically uniform nontrivial upper bounds for the aperiodic autocorrelation of these sequences are also given

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

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

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

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

miniaturization of microstrip antennas by the novel application of the giuseppe peano fractal geometries we investigate the possibilities and properties of the application of giuseppe peano fractal geometry for the miniaturization of microstrip patch antennas and compare its performance with those of the usual fractals such as koch tee type and sierpinski the length of the giuseppe peano fractal patch perimeter increases while its surface area remains constant without any more space occupation consequently the antenna miniaturization maintenance of its gain and increase of its relative frequency bandwidth are achieved the proposed antenna has circular polarization at one of its resonance frequencies which is realized by producing a perturbation on its initial structure further miniaturization of antenna may be obtained by cutting slots on its structure and its broadbanding may be achieved by placing an air gap under its metallic patch and more effective miniaturization is obtained by placing a giuseppe peano fractal strip along the microstrip patch antenna

fracture statistics of brittle materials weibull or normal distribution the fit of fracture strength data of brittle materials si3n4 sic and zno to the weibull and normal distributions is compared in terms of the akaike information criterion for si3n4 the weibull distribution fits the data better than the normal distribution but for zno the result is just the opposite in the case of sic the difference is not large enough to make a clear distinction between the two distributions there is not sufficient evidence to show that the weibull distribution is always preferred to other distributions and the uncritical use of the weibull distribution for strength data is questioned

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

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

static kinematic duality and the principle of virtual work in the mechanics of fractal media abstract the framework for the mechanics of solids deformable over fractal subsets is outlined while displacements and total energy maintain their canonical physical dimensions renormalization group theory permits to define anomalous mechanical quantities with fractal dimensions i e the fractal stress and the fractal strain e a fundamental relation among the dimensions of these quantities and the hausdorff dimension of the deformable subset is obtained new mathematical operators are introduced to handle these quantities in particular classical fractional calculus fails to this purpose whereas the recently proposed local fractional operators appear particularly suitable the static and kinematic equations for fractal bodies are obtained and the duality principle is shown to hold finally an extension of the gauss green theorem to fractional operators is proposed which permits to demonstrate the principle of virtual work for fractal media

a generalized model of elastic foundation based on long range interactions integral and fractional model abstract the common models of elastic foundations are provided by supposing that they are composed by elastic columns with some interactions between them such as contact forces that yield a differential equation involving gradients of the displacement field in this paper a new model of elastic foundation is proposed introducing into the constitutive equation of the foundation body forces depending on the relative vertical displacements and on a distance decaying function ruling the amount of interactions different choices of the distance decaying function correspond to different kind of interactions and foundation behavior the use of an exponential distance decaying function yields an integro differential model while a fractional power law decay of the distance decaying function yields a fractional model of elastic foundation ruled by a fractional differential equation it is shown that in the case of exponential decaying function the integral equation represents a model in which all the gradients of the displacement function appear while the fractional model is an intermediate model between integral and gradient approaches a fully equivalent discrete point spring model of long range interactions that may be used for the numerical solution of both integral and fractional differential equation is also introduced some green s functions of the proposed model have been included in the paper and several numerical results have been also reported to highlight the effects of long range forces and the governing parameters of the linear elastic foundation proposed

an improvement on the bounds of weil exponential sums over galois rings with some applications we present an upper bound for weil type exponential sums over galois rings of characteristic p sup 2 which improves on the analog of the weil carlitz uchiyama bound for galois rings obtained by kumar helleseth and calderbank 1995 a more refined bound expressed in terms of genera of function fields and an analog of mceliece s 1971 theorem on the divisibility of the homogeneous weights of codewords in trace codes over z sub p sup 2 are also derived these results lead to an improvement on the estimation of the minimum distance of certain trace codes over z sub p sup 2 and the bounds on the correlation of certain nonlinear p ary sequences

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

negacyclic and cyclic codes over z sub 4 the negashift spl nu of z sub 4 sup n is defined as the permutation of z sub 4 sup n such that spl nu a sub 0 a sub 1 spl middot spl middot spl middot a sub i spl middot spl middot spl middot a sub n 1 a sub n 1 a sub 0 spl middot spl middot spl middot a sub i spl middot spl middot spl middot a sub n 2 and a negacyclic code of length n over z sub 4 is defined as a subset c of z sub 4 sup n such that spl nu c c we prove that the gray image of a linear negacyclic code over z sub 4 of length n is a binary distance invariant not necessary linear cyclic code we also prove that if n is odd then every binary code which is the gray image of a linear cyclic code over z sub 4 of length n is equivalent to a not necessary linear cyclic code and this equivalence is explicitely described this last result explains and generalizes the existence already known of versions of kerdock preparata and others codes as doubly extended cyclic codes furthermore we introduce a family of binary linear cyclic codes which are gray images of z sub 4 linear negacyclic codes

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

an approach to solving mechanics problems for materials with multiscale self similar microstructure this article proposes an efficient method for solving mechanics boundary value problems formulated for domains with multiscale self similar microstructure in particular composite materials for which one of the phases has a fractal like structure with scale cut offs are considered the boundary value problems are solved using a finite element procedure with enriched shape functions that incorporate information about the geometric complexity the use of these shape functions makes possible the definition of a unique parametrically defined model from which the solution for configurations with an arbitrary number of scales can be derived the proposed method is primarily useful for structures with a large number of self similar scales for which using the usual finite element method would be too expensive in order to exemplify the method a 2d composite with fractal microstructure is considered and several boundary value problems are solved

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

quaternary constant amplitude codes for multicode cdma a constant amplitude code is a code that reduces the peak to average power ratio papr in multicode code division multiple access mc cdma systems to the favorable value 1 in this paper quaternary constant amplitude codes codes over z 4 of length 2 m with error correction capabilities are studied these codes exist for every positive integer m while binary constant amplitude codes cannot exist if m is odd every word of such a code corresponds to a function from the binary m tuples to z4 having the bent property i e its fourier transform has magnitudes 2 m 2 several constructions of such functions are presented which are exploited in connection with algebraic codes over z4 in particular quaternary reed muller kerdock and delsarte goethals codes to construct families of quaternary constant amplitude codes mappings from binary to quaternary constant amplitude codes are presented as well

spectral gap and transience for ruelle operators on countable markov shifts we find a necessary and sufficient condition for the ruelle operator of a weakly holder continuous potential on a topologically mixing countable markov shift to act with spectral gap on some rich banach space we show that the set of potentials satisfying this condition is open and dense for a variety of topologies we then analyze the complement of this set in a finer topology and show that among the three known obstructions to spectral gap weak positive recurrence null recurrence transience transience is open and dense and null recurrence and weak positive recurrence have empty interior

effective characteristics and stress concentrations in materials with self similar microstructure abstract it is proposed to model materials with self similar structure by a continuum sequence of continua of increasing scales each determined by its own size of the averaging volume element the scaling is represented by power laws with the exponents determined by the microstructure but not necessarily by the material fractal dimension the scaling laws for tensors are shown to be always isotropic the same exponent for all non zero components with the prefactors accounting for anisotropy for materials with self similar distributions of pores cracks and rigid inclusions the scaling laws for elastic characteristics were determined using the differential self consistent method stresses are defined in each continuum and are measured in conventional units of stress with the scaling law controlling the transition from one continuum to another i e from one stress field to another in the case of strong self similarity the scaling exponent for the stress field is uniform coincides with the one for the average nominal stress and is controlled by the sectional fractal dimension of the material within each continuum the stress concentrators point force dislocation semi infinite crack produce conventional stress singularities however as the point of singularity is approached the transition to finer continua is necessary resulting in some cases in apparent non conventional exponent of the stress increase

further result of compressing maps on primitive sequences modulo odd prime powers let be the integer residue ring with odd prime and integer for a sequence over there is an unique adic expansion where each is a sequence over and can be regarded as a sequence over the prime field gf naturally let be a strongly primitive polynomial over and the set of all primitive sequences generated by over suppose that gf gf it is shown that any function in is an injective map from to gf and the derived sequences of different functions are also different that is if and only if and for and these injective functions in can be considered as good candidates for the keys of a stream cipher

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

improved binary codes and sequence families from z sub 4 linear codes a bound on exponential sums over galois rings is used to construct a nested chain of z sub 4 linear binary codes and binary sequences when compared with the chain of delsarte goethals 1975 codes the codes in the new chain offer a larger minimum distance for the same code size the binary sequence families constructed also make use of nechaev s 1991 construction of a cyclic version of the kerdock code for a given value of maximum correlation the binary sequences are shown to have a family size considerably larger than the best sequence families known

sharp p divisibility of weights in abelian codes over bbz p d bbz a theorem of mceliece on the p divisibility of hamming weights in cyclic codes over fp is generalized to abelian codes over zopf p dzopf this work improves upon results of helleseth kumar moreno shanbhag calderbank li poonen wilson and katz these previous attempts are not sharp in general i e do not report the full extent of the p divisibility except in special cases nor do they give accounts of the precise circumstances under which they do provide best possible results this paper provides sharp results on p divisibilities of hamming weights and counts of any particular symbol for an arbitrary abelian code over zopf p dzopf it also presents sharp results on 2 divisibilities of lee and euclidean weights for abelian codes over zopf 4zopf

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

experimental validation of performance limits and design guidelines for small antennas the theoretical limit for small antenna performance that was derived decades ago by wheeler and chu governs design tradeoffs for size bandwidth and efficiency theoretical guidelines have also been derived for other details of small antenna design such as permittivity aspect ratio and even the nature of the internal structure of the antenna in this paper we extract and analyze experimental performance data from a large body of published designs to establish several facts that have not previously been demonstrated 1 the theoretical performance limit for size bandwidth and efficiency are validated by all available experimental evidence 2 although derived for electrically small antennas the same theoretical limit is also generally a good design rule for antennas that are not electrically small 3 the theoretical predictions for the performance due to design factors such as permittivity aspect ratio and the internal structure of the antenna are also supported by the experimental evidence the designs that have the highest performance are those that involve the lowest permittivity have an aspect ratio close to unity and for which the fields fill the minimum size enclosing sphere with the greatest uniformity this work thus validates the established theoretical design guidelines

fractional differentiation of devil s staircases abstract modern nonlinear dynamics abounds in mathematical objects with bizarre shapes and properties it is argued that fractional calculus provides powerful tools for the description of such monstrosities the application of generalized differintegration to devil s staircases is discussed in detail on the basis of these results an extension of the conventional classification scheme for phase transitions introducing fractional order is proposed

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

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

further results on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers this paper studies the distinctness of primitive sequences over z m modulo 2 where m is an odd integer that is composite and square free and z m is the integer residue ring modulo m a new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f x over z m are pairwise distinct modulo 2 such result improves a recent result obtained in our previous paper and consequently the set of primitive sequences over z m that can be proven to be distinct modulo 2 is greatly enlarged

the self similar field and its application to a diffusion problem we introduce a continuum approach which accounts for self similarity as a symmetry property of an infinite medium a self similar laplacian operator is introduced which is the source of self similar continuous fields in this way self similar symmetry appears in an analogous manner as transverse isotropy or cubic symmetry of a medium as a consequence of the self similarity the laplacian is a non local fractional operator obtained as the continuum limit of the discrete self similar laplacian introduced recently by michelitsch et al 2009 phys rev e 80 011135 the dispersion relation of the laplacian and its green s function is deduced in closed forms as a physical application of the approach we analyze a self similar diffusion problem the statistical distributions which constitute the solutions of this problem turn out to be levi stable distributions with infinite variances characterizing the statistics of one dimensional levi flights the self similar continuum approach introduced in this paper has the potential to be applied on a variety of scale invariant and fractal problems in physics such as in continuum mechanics electrodynamics and in other fields

upper bound for a hybrid sum over galois rings with applications to aperiodic correlation of some q ary sequences an upper bound for a hybrid exponential sum over galois rings is derived this bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over galois rings the bound is of the order of spl radic qlnq where q 1 is the period of the sequences

a re examination of the fundamental limits on the radiation q of electrically small antennas an exact method which is more straightforward than those previously published is derived for the calculation of the minimum radiation q of a general antenna this expression agrees with the previously published and widely cited approximate expression in the extreme lower limit of electrical size however for the upper end of the range of electrical size which is considered electrically small the exact expression given here is significantly different from the approximate expression this result has implications on both the bandwidth and efficiency limitations of antennas which fall into this category

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

improved estimates via exponential sums for the minimum distance of z sub 4 linear trace codes an upper hound for weil type exponential sums over galois rings was derived by kumar helleseth and calderbank see ibid vol 41 no 3 p 456 1995 this bound leads directly to an estimate for the minimum distance of z sub 4 linear trace codes an improved minimum distance estimate is presented first mceliece s result on the divisibility of the weights of binary cyclic codes is extended to z sub 4 trace codes the divisibility result is then combined with the techniques of serre 1983 and of moreno and moreno see ibid vol 40 no 11 p 1101 1994 to derive the improved minimum distance estimate the improved estimate is tight for the kerdock code as well as for the delsarte goethals codes

numerical solutions of two dimensional anisotropic crack problems a complete set of series form solutions of stress and displacement functions including all higher order terms around the crack tip for anisotropic crack problems have been newly derived by eigenfunction expansion approach the analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters and different corresponding physical meanings by employing these displacement functions as global interpolation functions fractal two level finite element method f2lfem was applied to evaluate the stress intensity factors sifs for various kinds of anisotropic crack problems in the method of f2lfem the infinite number of nodal displacements was transformed to a small set of generalized coordinates by fractal transformation technique new element matrices need not be generated and the singular numerical integration was avoided completely numerical examples of the four cases were studied and high accurate results of sifs were obtained

a new computational approach for solving nonlinear local fractional pdes abstract in this article we propose a new factorization technique for nonlinear odes involving local fractional derivatives for the first time by making use of the traveling wave transformation the exact solutions for nonlinear local fractional fitzhugh nagumo and newell whitehead equations are given the obtained results illustrate that the proposed method is efficient and accurate for finding the exact solutions for a class of local fractional pdes occurring in mathematical physics

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