augmented is lm model based on particular functions abstract in this paper we create our own static and dynamic augmented is lm model based on concrete particular functions these functions represent a mathematical and analytical description of economical quantities on which the is lm model is based and whose properties follow from the corresponding economical theories we prove several theorems about parameters of this model we describe dynamical behaviour of this system and prove un stability of the singular points including their classification then we demonstrate this model on some illustrative examples and we suggest our own econometric non linear regression models of the particular functions courses

generalized scaling in fully developed turbulence in this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows the limits of a new form of scaling named extended self similarity ess are discussed we show that when a mean shear is absent the self scaling exponents are universal and they do not depend on the specific flow 3d homogeneous turbulence thermal convection mhd in contrast ess is not observed when a strong shear is present we propose a generalized version of self scaling which extends down to the smallest resolvable scales even in cases where ess is not present this new scaling is checked in several laboratory and numerical experiments a possible theoretical interpretation is also proposed a synthetic turbulent signal having most of the properties of a real one has been generated

an efficient optimal normal basis type ii multiplier this paper presents a new parallel multiplier for the galois field gf 2 sup m whose elements are represented using the optimal normal basis of type ii the proposed multiplier requires 1 5 m sup 2 m xor gates as compared to 2 m sup 2 m xor gates required by the massey omura multiplier the time complexities of the proposed and the massey omura multipliers are similar

a stochastic dynamic model to evaluate the influence of economy and well being on unemployment control abstract this paper presents a stochastic dynamic mathematical model to study the evolution of the unemployment rate and other relevant related variables in a country this model is composed by three basic interrelated subsystems demographic economic and well being ones a key aspect of this model is that it considers three un well being variables simultaneously human development index gender empowerment index and gender differentiation index these variables involve key concepts for human development as health education economy and female labor with this model the most outstanding variables found in the literature in relation with unemployment control can be used to design strategies and scenarios to reduce the unemployment rate in the future the model has been fitted for the case of spain in the 2002 2014 period the largest one with information about all the variables involved in the model finally several tentative scenarios and strategies have been tested to reduce the unemployment rate in spain in the horizon of year 2025 and the corresponding forecast evolution of the gender differentiation index national income per capita public debt and the ratio between public debt and gross domestic product are shown

scaling hypothesis leading to extended self similarity in turbulence a scaling hypothesis leading to extended self similarity ess for structure functions the qth order moments of the magnitude of the longitudinal component velocity differences in isotropic homogeneous turbulence is proposed this is done by generalizing the scale variable r to rg r l with a crossover function g by extending the refined self similarity it is shown that the presented scaling also leads to ess for structure functions of the energy dissipation rate fluctuations and to ess bridging relations between velocity and dissipation rate moments extended self similarity on the basis of a universal crossover function g strictly holds toward the outer scale l range only yet we find at least approximate ess toward the viscous inner scale l range furthermore the probability densities for the velocity differences and the energy dissipation rate fluctuations which are compatible with this ess are offered

extended self similarity in the numerical simulation of three dimensional homogeneous flows we report the statistical analysis of several velocity configurations obtained by performing numerical simulations of three dimensional homogeneous incompressible turbulence this analysis provides full support to the idea recently proposed by benzi et al phys rev e 48 29 1993 that fluid flows exhibit extended self similarity a sort of generalized scale invariance which holds at high as well as at low to moderate reynolds numbers

p ary unified sequences p ary extended d form sequences with the ideal autocorrelation property in this paper for a prime number p a construction method to generate p ary d form sequences with the ideal autocorrelation property is proposed and using the ternary sequences found by helleseth kumar and martinsen 2000 ternary d form sequences with the ideal autocorrelation property are constructed by combining the methods for generating p ary extended sequences a special case of geometric sequences and p ary d form sequences a construction method of p ary unified extended d form sequences which also have the ideal autocorrelation property is proposed this is a very general class of p ary sequences including the binary and nonbinary extended sequences and the d form sequences from the ternary sequences by helleseth kumar and martinsen ternary unified sequences with the ideal autocorrelation property are also generated

maximal families of bent sequences in a recent paper olsen scholtz and welch osw describe the use of bent functions to construct families of sequences with asymptotically optimal correlation properties we show that the sequences produced by the osw construction possess the claimed correlation properties if and only if the underlying bent functions are pairwise orthogonal consequently the cardinality of a family of osw sequences of length 2 n 1 cannot exceed 2 n 2 we also describe methods of selecting a maximal set of orthogonal bent functions

a dynamic is lm business cycle model with two time delays in capital accumulation equation in this paper we analyze a augmented is lm business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to kalecki s idea applying stability switch criteria and hopf bifurcation theory we prove that time delays cause the equilibrium to lose or gain stability and hopf bifurcation occurs

character sum factorizations yield sequences with ideal two level autocorrelation we give a new existence criterion for p ary sequences which have ideal two level autocorrelation and we use it to obtain four general families of such sequences one for p 2 one for general odd primes p and two special ones for p 3 the binary family turns out to be equivalent to that discovered by dillon and dobbertin and published in 2004 the general p ary family is equivalent to that discovered by gong and helleseth by dillon and when p 3 by helleseth kumar and martinsen all of these p ary results were published in 2001 and 2002 the special ternary families are new and give as special cases the sequences conjectured by alfred lin in his 1998 ph d thesis as well as most of those conjectured in 2001 by ludkovski and gong our sequences may also be used to construct relative difference sets their corresponding block designs and generalized weighing matrices

fixed points imply chaos for a class of differential inclusions that arise in economic models we consider multi valued dynamical systems with continuous time of the form f x where f x is a set valued function such models have been studied recently in mathematical economics we provide a definition for chaos chaos and topological entropy for these differential inclusions that is in terms of the natural r action on the space of all solutions of the model by considering this more complicated topological space and its r action we show that chaos is the typical behavior in these models by showing that near any hyperbolic fixed point there is a region where the system is chaotic chaotic and has infinite topological entropy

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

von karman howarth equation for three dimensional two fluid plasmas we derive the von karman howarth equation for a full three dimensional incompressible two fluid plasma in the long time limit and for very large reynolds numbers we obtain the equivalent of the hydrodynamic four fifths law this exact law predicts the scaling of the third order two point correlation functions and puts a strong constraint on the plasma turbulent dynamics finally we derive a simple expression for the 4 5 law in terms of third order structure functions which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges

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

fast normal basis multiplication using general purpose processors for cryptographic applications normal bases have received considerable attention especially for hardware implementation we consider fast software algorithms for normal basis multiplication over the extended binary field gf 2 sup m we present a vector level algorithm which essentially eliminates the bit wise inner products needed in the conventional approach to the normal basis multiplication we then present another algorithm which significantly reduces the dynamic instruction counts both algorithms utilize the full width of the data path of the general purpose processor on which the software is to be executed we also consider composite fields and present an algorithm which can provide further speed ups and an added flexibility toward hardware software codesign of processors for very large finite fields

anisotropy and scaling corrections in turbulence we analyze second order turbulent velocity moments both in r and in p space finite size corrections induce dramatic differences between local r and p space scaling exponents as analytically accessible examples we focus on two popular parametrizations the batchelor parametrization for the r space structure function and a common parametrization for the energy spectrum e p is proportional to p 5 3exp p pd the spectral bottleneck energy pileup hidden in the batchelor parametrization results in an extended r space scaling range comparable to experimental ones for the same taylor reynolds number re lambda shear effects are discussed in terms of global apparent scaling correction delta zeta app re lambda to classical scaling which again depend on whether looked at in r or in p space the differences can be traced back to the subtleties of the crossovers in the velocity moments our observations emphasize the need for more experimental information on crossovers between different subranges

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

local properties of extended self similarity in three dimensional turbulence where the scaling exponent q is some function of q it is shown in numerous experiments and numerical simulations that the range of applicability of the ess is substantially larger than that for ordinary self similarity and the ess can exist even for situations where the ordinary self similarity cannot be observed at all the aim of the present letter is twofold the first is to study local properties of ess defined as h u pi u 3 p r 2 where p r are depending on r the local approach allows to develop some old ideas at past a representation p p 3 p p 3 18 derived from a lognormal model was shown to hold for the values averaged over an inertial interval of certain extension here we will show that the representation holds locally i e with p r and r depending on r in the above defined sense ranging from the dissipative kolmogorov length to integral scale for any observed reynolds number in direct numerical simulations up to r 459 the second aim is to examine the implication of the variation of the local intermittency exponent r it is often mentioned that there is no characteristic length in turbulence so that the structure functions obey a power law in the inertial region and the associated scaling exponents are independent of scale however a recent study of turbulence reveals the existence of the structures 9 a question then naturally arises as to whether there may be any characteristic length ascribed to the structures 10 the peculiar variation of r with respect to r observed in the letter indicates that there is a certain length affecting the ess the she leveque model 11 is also very popular in the last years for this model the local exponent is expressed in a general form

large families of sequences with near optimal correlations and large linear span in order to build spread spectrum communication systems based on the cdma paradigm it is necessary to have large families of binary sequences with low pairwise correlation values for these systems to have resistance to certain cryptanalytic attacks and resistance to jamming the sequences must have large linear span we describe certain families of sequences that have these desirable properties the sequences are based on families of quadratic forms over finite fields

on correlations of a family of generalized geometric sequences in this correspondence we study families of generalized geometric sequences formed bp applying a feedforward function to certain sums of decimated m sequences with elements in a finite field we compute their correlation functions which for certain families turn out to be close to the square root of the period the size of these families equals their period we also show that in the binary case the linear complexities of these sequences are much larger than those of cascaded geometric sequences although in these cases the maximum correlations are larger

on the linear complexity of some new q ary sequences some new q ary sequences with period q 3 e k 1 q p m p an odd prime m e k integers are first constructed and then inspired by antweiler s method their linear complexity is examined the exact value of linear complexity k 6e w is determined when email protected i 1 wp e i furthermore an upper bound of the linear complexity is given for the other values of r our results show that this sequence has larger linear span than gmw sequence with the same parameters finally the results of a maple program are included to illustrate the validity of the results

velocity structure functions scaling and transitions in high reynolds number couette taylor flow flow between concentric cylinders with a rotating inner cylinder is studied for reynolds numbers in the range 2 ifmmode times else texttimes fi 10 3 lrl 10 6 taylor reynolds numbers 10l r ensuremath lambda l290 for a system with radius ratio ensuremath eta 0 724 even at the highest reynolds number studied the energy spectra do not show power law scaling i e there is no inertial range and the dissipation length scale is surprisingly large nevertheless the velocity structure functions calculated using extended self similarity exhibit clear power law scaling the structure function exponents ensuremath zeta p fit kolmogorov s log normal model within the experimental uncertainty ensuremath zeta p p 3 1 ensuremath mu 6 3 ensuremath p for pl 10 with ensuremath mu 0 27 these ensuremath zeta p values are close to those found in other flows measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported lathrop et al phys rev a 46 6390 1992 measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest reynolds numbers examined these waves show evidence of a transition at r t 1 3 ifmmode times else texttimes fi 10 4 this transition was observed previously in measurements of torque but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at r t velocity measurements indicate that at r t there is a change in the coherent structures of the core flow this is consistent with our analyses of the scaling of the torque our measurements were made at two aspect ratios and no significant dependence on aspect ratio was observable for rg r t

spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence the pseudospectral method in conjunction with a technique for obtaining scaling exponents n from the structure functions sn r is presented as an alternative to the extended self similarity ess method and the use of generalized structure functions we propose plotting the ratio sn r s3 r against the separation r in accordance with a standard technique for analyzing experimental data this method differs from the ess technique which plots sn r against s3 r with the assumption s3 r r using our method for the particular case of s2 r we obtain the result that the exponent 2 decreases as the taylor reynolds number increases with 2 0 679 0 013 as r this supports the idea of finite viscosity corrections to the k41 prediction for s2 and is the opposite of the result obtained by ess the pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

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

analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay in this paper a delayed fractional order financial system is proposed and the complex dynamical behaviors of such a system are discussed by numerical simulations a great variety of interesting dynamical behaviors of such a system including single periodic multiple periodic and chaotic motions are displayed in particular the effect of time delay on the chaotic behavior is investigated it is found that an approximate time delay can enhance or suppress the emergence of chaos meanwhile corresponding to different values of delay the lowest orders for chaos to exist in the delayed fractional order financial systems are determined respectively

on the scaling of three dimensional homogeneous and isotropic turbulence abstract in this paper we investigate the scaling properties of three dimensional isotropic and homogeneous turbulence we analyze a new form of scaling extended self similarity recently introduced in the literature we found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low reynolds number and it extends over a much wider range of scales with respect to the inertial range

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

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

low complexity word level sequential normal basis multipliers for efficient hardware implementation of finite field arithmetic units the use of a normal basis is advantageous in this paper two classes of architectures for multipliers over the finite field gf 2 sup m are proposed these multipliers are of sequential type i e after receiving the coordinates of the two input field elements they go through k 1 spl les k spl les m iterations i e clock cycles to finally yield all the coordinates of the product in parallel the value of k depends on the word size w spl lceil m k spl rceil for w 1 these multipliers are highly area efficient and require fewer number of logic gates even when compared with the most area efficient multipliers available in the open literature this makes the proposed multipliers suitable for applications where the value of m is large but space is of concern e g resource constrained cryptographic systems additionally if the field dimension m is composite i e m kn then the extension of one class of the architectures yields a highly efficient multiplier over composite fields

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

bounds on partial correlations of sequences two approaches to bounding the partial auto and crosscorrelations of binary sequences are considered the first approach uses the discrete fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m sequences and on the partial auto and crosscorrelations for the small kasami sets and dual bch families of sequences the second approach applies to binary sequences obtained by interleaving m sequences a bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m sequences the bound is applied to gmw no 1987 and other families of sequences for particular parameters a comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable on the other hand both methods show that well known sequence families can have favorable partial correlation characteristics making them useful in certain spread spectrum applications

divisible difference sets relative difference sets and sequences with ideal autocorrelation abstract in this correspondence we consider the equivalent condition that a sequence possesses ideal autocorrelation function as we know for a binary sequence the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets this paper proves that for a p ary sequence with d form property the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p 1 relative difference sets moreover a new way to construct cyclic divisible difference sets is presented

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

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

wg a family of stream ciphers with designed randomness properties in this paper we present a family of stream ciphers which generate a keystream with ideal two level autocorrelation the design also guarantees other randomness properties i e balance long period ideal tuple distribution and high and exact linear complexity we discuss how these properties are achieved by the proposed design and show how to select various parameters to obtain an efficient stream cipher for the desired security level we also show that the proposed generators are secure against time memory data tradeoff attacks algebraic attacks and correlation attacks finally we present wg 128 as a concrete example of a wg stream cipher with a key size of 128bits

vlsi architectures for computing multiplications and inverses in gf 2 m finite field arithmetic logic is central in the implementation of reed solomon coders and in some cryptographic algorithms there is a need for good multiplication and inversion algorithms that can be easily realized on vlsi chips massey and omura 1 recently developed a new multiplication algorithm for galois fields based on a normal basis representation in this paper a pipeline structure is developed to realize the massey omura multiplier in the finite field gf 2m with the simple squaring property of the normal basis representation used together with this multiplier a pipeline architecture is also developed for computing inverse elements in gf 2m the designs developed for the massey omura multiplier and the computation of inverse elements are regular simple expandable and therefore naturally suitable for vlsi implementation

statistics of turbulent fluctuations in counter rotating taylor couette flows the statistics of velocity fluctuations of turbulent taylor couette flow are examined the rotation rates of the inner and outer cylinders are varied while keeping the taylor number fixed to 1 49 10 12 o re 10 6 the azimuthal velocity component of the flow is measured using laser doppler anemometry for each experiment 5 10 6 data points are acquired and carefully analyzed using extended self similarity benzi et al phys rev e 48 r29 1993 the longitudinal structure function exponents are extracted and are found to weakly depend on the ratio of the rotation rates for the case where only the inner cylinder rotates the results are in good agreement with results measured by lewis and swinney phys rev e 59 5457 1999 using hot film anemometry the power spectra show clear 5 3 scaling for the intermediate angular velocity ratios o i 0 6 0 8 1 0 roughly 5 3 scaling for o i 0 2 0 3 0 4 2 0 and no clear scaling law can be found for 0 i 0 inner cylinder rotation only the local scaling exponent of the spectra has a strong frequency dependence we relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line

generalization of gmw sequences and no sequences gmw sequences and families of no sequences are generalized generalized gmw sequences have ideal autocorrelation and balance properties and generalized no sequences also have optimal correlation properties in terms of welch s lower bound the linear spans of the generalized gmw and no sequences appear to be large although there is not at present a closed form expression for the linear span a count of the numbers of cyclically distinct generalized gmw sequences and generalized no sequences that can be constructed is provided generalized gmw sequences have also been found in the literature by klapper et al 1993 under the name cascaded gmw sequences

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

scaling of the irreducible so 3 invariants of velocity correlations in turbulence the scaling behavior of the so 3 irreducible amplitudes d n r of velocity structure tensors is numerically examined for navier stokes turbulence here l characterizes the irreducible representation by the index of the corresponding legendre polynomial and n denotes the tensorial rank i e the order of the moment for moments of different order n but with the same representation index l extended self similarity ess towards large scales is found intermittency seems to increase with l we estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable reynolds numbers

application of extended self similarity in turbulence from navier stokes turbulence numerical simulations we show that for the extended self similarity ess method it is essential to take the third order structure function taken with the modulus and called d 3 r rather than the standard third order structure function d3 r itself if this is done we find ess towards scales larger than order 10 eta where eta is the kolmogorov scale if d3 r is used there is no ess we also analyze ess within the batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function the re asymptotic inertial range scaling develops only beyond a taylor reynolds number re lambda 500

existence of chaos in the plane r 2 and its application in macroeconomics the existence of devaney li yorke and distributional chaos in the plane r 2 the chaos in a continuous dynamical system generated by euler equation branching all combinations of hyperbolic singular points of both branches admit chaos the chaotic set of solutions associated with chaotic subset of r 2 exists new overall macroeconomic equilibrium model called is lm qy ml model the existence of chaos in an economy the devaney li yorke and distributional chaos in the plane r 2 can occur in the continuous dynamical system generated by euler equation branching euler equation branching is a type of differential inclusion x f x g x where f g x r n r n are continuous and f x g x in every point x x stockman and raines 2010 defined the so called chaotic set in the plane r 2 whose existence leads to the existence of devaney li yorke and distributional chaos in this paper we follow up on stockman and raines 2010 and we show that chaos in the plane r 2 is always admitted for hyperbolic singular points in both branches not lying in the same point in r 2 but the chaos existence is also caused by a set of solutions of euler equation branching we research this set of solutions in the second part we create the new overall macroeconomic equilibrium model called is lm qy ml model this model is based on the fundamental macroeconomic equilibrium model called is lm model we model an inflation effect an endogenous money supply an economic cycle etc in addition to the original is lm model we research the dynamical behaviour of this new is lm qy ml model and show when a chaos exists with relevant economic interpretation

transition between viscous and inertial range scaling of turbulence structure functions the transition of velocity structure functions between the viscous and inertial range is examined by assuming a plausible interpolation formula for the required scaling functions this analysis shows that the recently observed phenomenon of extended self similarity ess is consistent with assuming that the cutoff length decreases with increasing order of the moment a revised multifractal formalism is used to quantify this dependence of cutoff scale on the order of the moment at low and intermediate reynolds numbers the proposed mechanism predicts ess as well as some additional subtle trends that are experimentally observed however at large reynolds numbers the shift in cutoff scale predicted by the multifractal formalism becomes too large to be consistent with ess textcopyright 1996 the american physical society

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

a new construction of massey omura parallel multiplier over gf 2 sup m the massey omura multiplier of gf 2 sup m uses a normal basis and its bit parallel version is usually implemented using m identical combinational logic blocks whose inputs are cyclically shifted from one another in the past it was shown that for a class of finite fields defined by irreducible all one polynomials the parallel massey omura multiplier had redundancy and a modified architecture of lower circuit complexity was proposed in this article it is shown that not only does this type of multiplier contain redundancy in that special class of finite fields but it also has redundancy in fields gf 2 sup m defined by any irreducible polynomial by removing the redundancy we propose a new architecture for the normal basis parallel multiplier which is applicable to any arbitrary finite field and has significantly lower circuit complexity compared to the original massey omura normal basis parallel multiplier the proposed multiplier structure is also modular and hence suitable for vlsi realization when applied to fields defined by the irreducible all one polynomials the multiplier s circuit complexity matches the best result available in the open literature

studies on the distribution of the shortest linear recurring sequences the distribution of the shortest linear recurrence slr sequences in the z p field and over the z p e ring is studied it is found that the length of the shortest linear recurrent slrl is always equal to n 2 if n is even and n 2 1 if n is odd in the z p field respectively on the other hand over the z p e ring the number of sequences with length n can also be calculated the recurring distribution regulation of the shortest linear recurring sequences is also found to solve the problem of calculating the slrl a new simple representation of the berlekamp massey algorithm is developed as well

new nonbinary sequences with ideal two level autocorrelation we find new families of nonbinary sequences of period p sup n 1 with symbols from a finite field f sub p for any prime p spl ges 3 the sequences have two level ideal autocorrelation and are generalizations of previously found ternary sequences with ideal autocorrelation difference sets with parameters p sup n 1 p 1 p sup n 1 1 p 1 p sup n 2 1 p 1 can also be derived from these sequences in a natural way

small scale intermittency and bursting in a turbulent channel flow the statistical properties of the streamwise velocity fluctuations in a fully developed turbulent channel flow are studied experimentally by means of single hot wire measurements the intermittency features studied through the scaling of the moments of the velocity structure function computed using the extended selfsimilarity and through the probability density function of the wavelet coefficients are found to be dependent on the distance from the wall the maximum intermittency effects are observed in the region between the buffer layer and the inner part of the logarithmic region where it is known that the bursting phenomenon related to coherent structures such as low speed streaks and streamwise vortices is the dominant dynamical feature an eduction technique based on wavelet transform for identification of organized motion is developed and used to analyze the turbulent signals streamwise velocity conditional averages computed on events educed with the proposed method are reported events responsible for intermittency are found to consist of regions of high velocity gradients and are directly correlated with the observed increase of intermittency close to the wall pacs number s 47 27 nz 01 50 pa i introduction a background

new sets of optimal p ary low correlation zone sequences in this correspondence three methods of constructing low correlation zone lcz sequences are proposed in the first method we constructed binary lcz sequence sets of period 2n 1 using the legendre sequences of period 2m 1 as a column sequence when m n in the second method we devise a column sequence set of length 2m 1 1 from a binary sequence of period 2m 1 having ideal autocorrelation property and this column sequence set is used to construct binary lcz sequence sets of period 2 n 1 when m 1 n in the third method p ary lcz sequence sets are constructed by adopting p ary sequence of period pm 1 with ideal autocorrelation for integers n and m such that m n as a column sequence the second and third methods give us the optimal sets with respect to the bound by tang fan and matsufuji finally a construction method of pntimespn p ary hadamard matrices from optimal lcz sequence sets is proposed

fluctuations of a passive scalar in a turbulent mixing layer the turbulent flow originating downstream of the kelvin helmholtz instability in a mixing layer has great relevance in many applications ranging from atmospheric physics to combustion in technical devices the mixing of a substance by the turbulent velocity field is usually involved in this paper a detailed statistical analysis of fluctuations of a passive scalar in the fully developed region of a turbulent mixing layer from a direct numerical simulation is presented passive scalar spectra show inertial ranges characterized by scaling exponents ensuremath 4 3 and ensuremath 3 2 in the streamwise and spanwise directions in agreement with a recent theoretical analysis of passive scalar scaling in shear flows celani et al j fluid mech 523 99 2005 scaling exponents of high order structure functions in the streamwise direction show saturation of intermittency with an asymptotic exponent ensuremath zeta ensuremath infty 0 4 at large orders saturation of intermittency is confirmed by the self similarity of the tails of the probability density functions of the scalar increments at different scales r with the scaling factor r ensuremath ensuremath zeta ensuremath infty and by the analysis of the cumulative probability of large fluctuations conversely intermittency saturation is not observed for the spanwise increments and the relative scaling exponents agree with recent results for homogeneous isotropic turbulence with mean scalar gradient probability density functions of the scalar increments in the three directions are compared to assess anisotropy

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

exponents of the structure functions in a low temperature helium experiment abstract we report new measurements of longitudinal structure function exponents in fully developed turbulence the measurements are performed in low temperature helium for a wide range of microscale reynolds numbers from 150 to 5040 using large velocity records up to 1010 points for the largest one i e 3 106 integral time scales exponents of the longitudinal structure function of the velocity denoted by p are determined in general up to tenth order and in one case up to twelfth order they are slightly smaller than previously reported values and it is safe to say that within the accuracy of the present measurements they do not seem to evolve significantly with the reynolds number high order values of p obtained by extrapolating the distributions of the velocity increments are determined for the largest record they are found to decrease with p above p 18

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

a generalized dynamic is lm model with delayed time in investment processes abstract in this paper we analyze a generalized dynamic is lm model with a government expenditure constraint and the capital accumulation equation that capital stock changes are caused by past investment decisions according to kalecki s idea of time delay in investment processes applying stability switch criteria we prove that the time delay causes the equilibrium point may lose or gain local stability so that the hopf bifurcation occurs

new hardware implementationsof wg bf 29 11 and wg bf 16 streamciphers using polynomial basis the wg stream ciphers are based on the wg welch gong transformation and possess proved randomness properties in this paper we propose nine new hardware designs for the two classes of wg 29 11 and wg 16 for each class we design and implement three versions of standard pipelined and serial for the first time we use the polynomial basis pb representation to design and implement the wg 29 11 and wg 16 we consider traditional pb multiplier for the wg 29 11 and the traditional and karatsuba multipliers for the wg 16 for efficient field operations we propose an irreducible trinomial for the wg 29 11 for the wg 16 a new formulation of its permutation which requires only 8 multipliers is introduced in these designs the multipliers in the transforms arefurther reduced by utilizing a novel computation for the trace of the multiplication of two field elements we have implemented theproposed designs in asic using cmos 65 nm technology the results show that the proposed standard wg 29 11 consumes less area and slightly enhances the normalized throughput compared to the existing counterparts for the wg 16 throughput of theproposed pipelined instance outperforms the previous designs moreover the speed of the proposed wg 16 designs meet the peak bit rates for the 4 g specifications

a general construction of binary interleaved sequences of period 4n with optimal autocorrelation abstract a general construction of binary interleaved sequences of period 4 n with low autocorrelation are considered in the paper firstly some correlation properties of two general classes of binary interleaved sequences are presented secondly based on these results autocorrelation functions of a general construction of binary interleaved sequences of period 4 n are given finally we show that from these results for general cases several known binary sequences of these types with optimal autocorrelation and some other new binary sequences with low autocorrelation can be constructed

complex sequences over gf p sup m with a two level autocorrelation function and a large linear span new complex sequences with elements are proposed that have constant absolute values of 1 the periodic autocorrelation functions of these sequences are shown to be two level the sequences are generated by three consecutive mapping processes the number of sequences of fixed length is determined which is larger than the number of binary sequences for cryptographical reasons the large linear span of the sequences is of great interest the linear span of the new sequences is examined and is proven to be larger than the linear span of complex m sequences if the parameters of the mapping processes are appropriately chosen the formula for generating the sequences is generalized to enlarge the linear span of sequences

the proof of lin s conjecture via the decimation hadamard transform in 1998 lin presented a conjecture on a class of ternary sequences with ideal two level autocorrelation those sequences have a very simple structure i e their trace representation has two trace monomial terms in this paper we present a proof for the conjecture the mathematical tools employed are the second order multiplexing decimation hadamard transform stickelberger s theorem the teichmuller character and combinatorial techniques for enumerating the hamming weights of ternary numbers as a by product we also prove that the ternary sequences conjectured by lin are hadamard equivalent to ternary m sequences

new constructions for optimal sets of frequency hopping sequences in this paper two generic constructions of optimal frequency hopping sequence fhs sets employing d form functions with difference balanced property are presented they generalize the previous constructions of optimal fhs sets using m sequences and produce new optimal fhs sets that cannot be produced by the earlier constructions by choosing appropriate d form functions with difference balanced property both constructions lead to fhss with large linear complexity in addition one of the proposed constructions gives new optimal parameters of fhs sets

a three valued walsh transform from decimations of helleseth gong sequences the walsh transform of two level autocorrelation sequences has played an important role in the construction of the set of sequences in which any two sequences are orthogonal for p ary sequences there are only two basic classes of two level autocorrelation sequences with no subfield structures for an arbitrary odd prime p one is the class of p ary m sequences and the other is the class of p ary helleseth gong sequences in this paper the walsh transform of a subclass of p ary helleseth gong sequences and the walsh transform of their particular decimations are completely determined and are shown to be three valued

cryptographic properties of the welch gong transformation sequence generators welch gong wg transformation sequences are binary sequences of period 2 sup n 1 with two level autocorrelation these sequences were discovered by golomb gong and gaal 1998 and they verified the validity of their construction for 5 spl les n spl les 20 later no chung and yun 1998 found another way to construct the wg sequences and verified their result for 5 spl les n spl les 20 dillon 1998 first proved this result for odd n and finally dobbertin and dillon 1999 proved it for even n in this paper we investigate a two faced property of the wg transformation sequences for application in stream ciphers and pseudorandom number generators one is to present the randomness or unpredictability of the wg transformation sequences the other is to exhibit the security properties of the wg transformations regarded as boolean functions in particular we prove that the wg transformation sequences in addition to the known two level autocorrelation and three level cross correlation with m sequences have the ideal 2 tuple distribution and large linear span increasing exponentially with n moreover it can be implemented efficiently this is the first type of pseudorandom sequences with good correlation statistic properties large linear span and efficient implementation when wg transformations are regarded as boolean functions they have high nonlinearity we derive a criterion for the boolean representation of wg transformations to be r resilient and show that they are at least 1 resilient under some basis of the finite field gf 2 sup n an algorithm to find such bases is given the degree and linear span of wg transformations are presented as well

some results on cross correlation distribution between a p ary m sequence and its decimated sequences for an odd prime p and two positive integers m k such that m gcd k m 3 is odd let d be a positive integer satisfying d p k 1 2 mod p m 1 i n this paper the cross correlation between a p ary m sequence and its d decimated sequences is investigated and the cross correlation distribution is completely determined the relationship between the decimations d considered in this paper and some known ones is also studied this paper generalizes some previous results and also gives new decimations which lead to low cross correlation