sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

new families of binary sequences with optimal three level autocorrelation in this correspondence we give several new families of binary sequences of period n with optimal three level autocorrelation where n spl equiv 2 mod 4 these sequences are either balanced or almost balanced our construction is based on cyclotomy

mixed type solutions of the su 3 models on a torus in this paper we study mixed type solutions of su 3 chern simons system see 1 4 below on a two dimensional flat torus nolasco and tarantello commun math phys 213 599 639 2000 among other things nolasco and tarantello obtained solutions of 1 4 as minimizers of several functionals closely related to 1 4 and showed that if n 1 n 2 1 then one of those minimizers turns out to be a mixed type solution that is one component tends to ln frac 1 2 pointwise a e and the other component converges to a solution of a mean field equation we call these kinds of solutions mixed type i solutions in this paper we prove two main results i the asymptotic analysis of mixed type i solutions with arbitrary configuration of vortex points and ii the existence of mixed type i solutions under a non degenerate condition this non degenerate condition also ensures some uniqueness result in particular our results imply that when n 1 n 2 1 there are only two mixed type i solutions of 1 4

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

a singular sphere covering inequality uniqueness and symmetry of solutions to singular liouville type equations we derive a singular version of the sphere covering inequality which was recently introduced in gui and moradifam invent math https doi org 10 1007 s00222 018 0820 2 2018 suitable for treating singular liouville type problems with superharmonic weights as an application we deduce new uniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains as well as new self contained proofs of previously known results such as the uniqueness of spherical convex polytopes first established in luo and tian proc am math soc 116 4 1119 1129 1992 furthermore we derive new symmetry results for the spherical onsager vortex equation

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

theory and applications of q ary interleaved sequences a new class of q ary sequences called interleaved sequence is introduced their periods shift equivalence linear spans and autocorrelation functions are derived the interleaved sequences include a large number of popular sequences such as multiplexed sequences clock controlled sequences kasami 1966 sequences gmw sequences geometric sequences and no 1989 sequences a special class of the interleaved sequences is constructed by mapping gf q sup m sequences into gf q sequences in terms of different bases of gf q sup m over gf q as an application of the theory of interleaved sequences some new families of binary pseudo random sequences are constructed which have large linear spans optimal periodic cross autocorrelation functions balance and the rapidly hopped properties a complete comparison of the new family of sequences with the gold sequence family the kasami small and large set sequence families the bent function sequence family and the no sequence family is discussed this shows that the new sequence families have important advantages for use in spread spectrum multiple access communication systems

mean field equation of liouville type with singular data topological degree we consider the following mean field equation gv h ev mh ev 1 4 j 1n j qj 1 on m where m is a compact riemann surface with volume 1 h is a positive c1 function on m and and j are constants satisfying j 1 in this paper we derive the topological degree counting formula for noncritical values of we also give several applications of this formula including existence of the curvature 1 metric with conic singularities doubly periodic solutions of electroweak theory and a special case of self gravitating strings 2015 wiley periodicals inc

on the mean field type bubbling solutions for chern simons higgs equation abstract this paper is the second part of our comprehensive study on the structure of the solutions for the following chern simons higgs equation 0 1 u 1 e 2 e u 1 e u 4 j 1 n p j in u is doubly periodic on where is a parallelogram in r 2 and e 0 is a small parameter in part 1 29 we proved the non coexistence of different bubbles in the bubbling solutions and obtained an existence result for the chern simons type bubbling solutions under some nearly necessary conditions mean field type bubbling solutions for 0 1 have been constructed in 27 in this paper we shall study two other important issues for the mean field type bubbling solutions the necessary conditions for the existence and the local uniqueness the results in this paper lay the foundation to find the exact number of solutions for 0 1

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

existence and multiplicity result for the singular toda system abstract we consider the toda system on a compact surface g u 1 2 1 h 1 e u 1 h 1 e u 1 d v g 1 2 h 2 e u 2 h 2 e u 2 d v g 1 4 j 1 j 1 j p j 1 u 2 2 2 h 2 e u 2 h 2 e u 2 d v g 1 1 h 1 e u 1 h 1 e u 1 d v g 1 4 j 1 j 2 j p j 1 where h i are smooth positive functions i are positive real parameters p j are given points on and i j are numbers greater than 1 we give existence and multiplicity results using variational and morse theoretical methods it is the first existence result when some of the i j s are allowed to be negative

new constructions of binary sequences with optimal autocorrelation value magnitude in this paper we give three new constructions of binary sequences of period an with optimal autocorrelation value or optimal autocorrelation magnitude using n 4 interleaved sequences yu and gong recently found any binary sequence of period an with optimal autocorrelation value constructed from an almost difference set by arasu et al is an n 4 interleaved sequence for which all four columns in its n 4 array are shift equivalent up to the complement we found that it is not necessary that four columns are shift equivalent instead it could be a pair of related sequences together with their shifts as the column sequences the first construction is to use a generalized gmw sequence of period n 2k 1 and its modified version the second construction is to use a twin prime sequence of length n p p 2 and its modified version and the third construction a pair of legendre sequences of period n p p odd prime with their respective first terms complementary the 2 level autocorrelation property is not needed for the legendre sequence the comparison with the known constructions are given for the new sequences with optimal autocorrelation value their corresponding new almost difference sets are also derived

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

elliptic functions green functions and the mean field equations on tori we show that the green functions on flat tori can have either 3 or 5 critical points only there does not seem to be any direct method to attack this problem instead we have to employ sophisticated non linear partial differential equations to study it we also study the distribution of number of critical points over the moduli space of flat tori through deformations the functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori the general picture is also emerged though some of the necessary technicality is still to de developed 1 introduction and statement of results the study of geometric or analytic problems on two dimensional tori is the same as the study of problems on r 2 with doubly periodic data such situations occur naturally in sciences and mathematics since early days the mathematical foundation of elliptic functions was subsequently devel oped in the 19th century it turns out that these special functions are rather deep objects by themselves tori of different shape may result in very dif ferent behavior of the elliptic functions and their associated objects arith metic on elliptic curves is perhaps the eldest and the most vivid example in this paper we show that this is also the case for certain non linear par tial differential equations indeed researches on doubly periodic problems in mathematical physics or differential equations often restrict the study to rectangular tori for simplicity this leaves the impression that the theory for general tori may resemble much the same way as for the rectangular case however this turns out to be false we will show that the solvability of themean field equation dependson the shape of the green function which in turn depends on the geometry of the tori in an essential way recall that the green function g z w on a flat torus t c z 1 z 2 is the unique function on t t which satisfies zg z w w z 1 t

new classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value sequences with optimal autocorrelation property are needed in certain communication systems and cryptography in this paper a construction of balanced quaternary sequences with period n 2 mod 4 and optimal autocorrelation value and a construction of almost balanced binary sequences with period n 0 mod 4 and optimal autocorrelation value are presented both constructions are a generalization of earlier ones

the linear complexity of binary sequences with optimal autocorrelation binary sequences with optimal autocorrelation are needed in many applications two constructions of binary sequences with optimal autocorrelation of period n 0 mod 4 are investigated the two constructions are powerful and generic in the sense that many classes of binary sequences with optimal autocorrelation could be obtained from binary sequences with ideal autocorrelation general results on the minimal polynomials of these binary sequences are derived based on the results both the linear complexities and the minimal polynomials are determined

binary and quadriphase sequences with optimal autocorrelation properties a survey time discrete signals with good autocorrelation properties are used in various applications in communications engineering from an implementation point of view usually sequences with a small phase alphabet and a maximal energy efficiency i e a uniform envelope are most favorable for this reason known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence in many cases the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted these almost binary and almost quadriphase sequences are considered as well the optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd periodic autocorrelation function respectively for sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case the best known parameters obtained by computer search are compared with the constructed results

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

new families of binary sequence pairs with two level and three level correlation a pair of binary sequences is generalized from the concept of a two level autocorrelation function of a single binary sequence in this paper new families of binary sequence pairs with period n np where gcd n p 1 and optimal correlation values 1 are constructed as well as new families of binary sequence pairs with three level correlation and period n 0 mod 4 for the new binary sequence pairs with optimal correlation values their corresponding new difference set pairs and almost difference set pairs are also derived

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

on the linear span of binary sequences obtained from q ary m sequences q odd a class of periodic binary sequences that are obtained from q ary m sequences is defined and a general method to determine their linear spans the length of the shortest linear recursion over the galois field gf 2 satisfied by the sequence is described the results imply that the binary sequences under consideration have linear spans that are comparable with their periods which can be made very long one application of the results shows that the projective and affine hyperplane sequences of odd order both have full linear span another application involves the parity sequence of order n which has period p sup m 1 where p is an odd prime the linear span of a parity sequence of order n is determined in terms of the linear span of a parity sequence of order 1 and this leads to an interesting open problem involving primes

patterson wiedemann type functions on 21 variables with nonlinearity greater than bent concatenation bound nonlinearity is one of the most challenging combinatorial property in the domain of boolean function research obtaining nonlinearity greater than the bent concatenation bound for odd number of variables continues to be one of the most sought after combinatorial research problems the pioneering result in this direction has been discovered by patterson and wiedemann in 1983 ieee it which considered boolean functions on 5 times 3 15 variables that are invariant under the actions of the cyclic group gf 2 5 ast cdot gf 2 3 ast as well as the group of frobenius automorphisms some of these boolean functions possess nonlinearity greater than the bent concatenation bound the next possible option for exploring such functions is on 7 times 3 21 variables however obtaining such functions remained elusive for more than three decades even after substantial efforts as evident in the literature in this paper we exploit combinatorial arguments together with heuristic search to demonstrate such functions for the first time

existence and non existence results for the su 3 singular toda system on compact surfaces we consider the su 3 singular toda system on a compact surface g u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 4 m 1m 1m pm 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 4 m 1m 2m pm 1 where hi are smooth positive functions on i r pm and im 1 we give both existence and non existence results under some conditions on the parameters i and im existence results are obtained using variational methods which involve a geometric inequality of new type non existence results are obtained using blow up analysis and localized poho aev type identities

primitive polynomials and m sequences over gf q sup m procedures for obtaining primitive polynomials and m sequences over gf q sup m in terms of primitive polynomials and m sequences over gf q are presented using a degree mn primitive polynomial g x in gf g x an m sequence over gf q sup m can be expressed as a vector m sequence whose component m sequences are shifted versions of the m sequence generated by g x the degree n primitive polynomials in gf q sup m x with root alpha q sup i that are factors of g x with root alpha when g x is viewed in gf q sup m x are then developed from the m sequence over gf q sup m expressions for the shifts and corresponding primitive polynomial for the m sequence generated by the uth decimation of the m sequence generated by the polynomials are also given expressions for the shifts and corresponding primitive polynomial factors of g x for different bases expressing gf q sup m over gf q are presented

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

strategic attack on the shrinking generator the shrinking generator is a simple keystream generator with applications in stream ciphers which is still considered as a secure generator this work shows that in order to cryptanalyze it fewer intercepted bits than indicated by the linear complexity are necessary indeed whereas the linear complexity of shrunken sequences is between email protected 2 s 2 and email protected 2 s 1 we claim that the initial states of both component registers are easily computed with fewer than email protected s shrunken bits located at particular positions such a result is proven thanks to the definition of shrunken sequences as interleaved sequences consequently it is conjectured that this statement can be extended to all interleaved sequences furthermore this paper confirms that certain bits of the interleaved sequences have a greater strategic importance than others which must be considered as a proof of weakness of interleaved generators

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

non degeneracy and uniqueness of solutions to singular mean field equations on bounded domains abstract the aim of this paper is to complete the program initiated in 51 23 and then carried out by several authors concerning non degeneracy and uniqueness of solutions to mean field equations in particular we consider mean field equations with general singular data on non smooth domains the argument is based on the alexandrov bol inequality and on the eigenvalues analysis of linearized singular liouville type problems

the liouville equation with singular data a concentration compactness principle via a local representation formula abstract for a bounded domain r 2 we establish a concentration compactness result for the following class of singular liouville equations u e u 4 j 1 m j p j in where pj j 0 and pj denotes the dirac measure with pole at point pj j 1 m our result extends brezis merle s theorem comm partial differential equations16 1991 1223 1253 concerning solution sequences for the regular liouville equation where the dirac measures are replaced by lp data p 1 in some particular case we also derive a mass quantization principle in the same spirit of li shafrir indiana univ math j 43 1994 1255 1270 our analysis was motivated by the study of the bogomol nyi equations arising in several self dual gauge field theories of interest in theoretical physics such as the chern simons theory self dual chern simons theories lecture notes in physics vol 36 springer verlag berlin 1995 and the electroweak theory selected papers on gauge theory of weak and electromagnetic interactions world scientific singapore

uniqueness of bubbling solutions with collapsing singularities abstract the seminal work 7 by brezis and merle showed that the bubbling solutions of the mean field equation have the property of mass concentration recently lin and tarantello in 30 found that the bubbling implies mass concentration phenomena might not hold if there is a collapse of singularities furthermore a sharp estimate 23 for the bubbling solutions has been obtained in this paper we prove that there exists at most one sequence of bubbling solutions if the collapsing singularity occurs the main difficulty comes from that after re scaling the difference of two solutions locally converges to an element in the kernel space of the linearized operator it is well known that the kernel space is three dimensional so the main technical ingredient of the proof is to show that the limit after re scaling is orthogonal to the kernel space

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

asymptotic blow up analysis for singular liouville type equations with applications abstract we generalize the pointwise estimates obtained in 2 19 and 34 concerning blow up solutions of the liouville type equation u x 2 w x e u in with r 2 open and bounded 1 and w any lipschitz continuous function which satisfies 0 a w b we focus to the case left open in 2 and 34 where the parameter n whose analysis is much more involved as we need to resolve the difficulty of a genuinely non radial behaviour of blow up solutions in the worst situation there is no chance in general to resolve the profile in the form of a solution of a liouville equation in r 2 instead we need to adopt iterated blow up arguments next we refine our blow up analysis to cover a class of planar liouville type problems see 1 27 1 28 below arising from the study of cosmic strings cfr 28 35 in this context we are able to distinguish between a single blow up radial profile and the case of multiple blow up profiles typical of non radial solutions as a consequence we obtain a radial symmetry result which is interesting in itself but also contributes towards the sharp solvability issue for the planar problem 1 27 1 28

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

local solution acceleration method for the euler and navier stokes equations the solution of the compressible euler and navier stokes equations via an upwind finite volume scheme is obtained for the inviscid fluxes the monotone upstream centered scheme for conservation laws muscl has been incorporated into a riemann solver the muscl scheme is used for the unfactored implicit equations that are solved by a newton form and relaxation is performed via gauss seidel relaxation technique the solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid since the distribution of the numerical error is nonuniform the local solution of the equations can be obtained in regions where the numerical errors are large the construction of the partial meshes in which the iterations will be continued is determined by an adaptive procedure taking into account some convergence criteria reduction of the computational work units for two dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three dimensional complex flow computations

a priori estimates for d4 and f4 toda systems abstract in this article we establish the a priori bounds of the toda systems with arbitrarily many singular sources associated to the simple lie algebras of type d 4 and f 4 extending the previous works of lin et al 27 20 24 for the a n b n c n and g 2 type lie algebras the problem of obtaining a priori estimates can be reduced to locating the local mass of blowup solutions the key step is to calculate the local mass near each blowup points efficiently a precise estimate on the total mass of entire solutions of toda systems with many singular sources is an indispensable step in our argument

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

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

new construction for binary sequences of period p sup m 1 with optimal autocorrelation using z 1 sup d az sup d b we present a construction for binary sequences s t of period n p sup m 1 for an odd prime p based on the polynomial z 1 sup d az sup d b and discuss them in some cases of parameters p m d a and b we show that new sequences from our construction are balanced or almost balanced and have optimal three level autocorrelation for the case when the polynomial z 1 sup d z sup d a can be transformed into the form z sup 2 c we also derive the distribution of autocorrelation values they take on the sequences satisfy constant on the coset property and we show that there are more than one characteristic phases with constant on the coset property some other interesting properties of those sequences are presented for the cases when the polynomial z 1 sup d z sup d a cannot be transformed into the form z sup 2 c we performed extensive computer search and results are summarized based on these results some open problems are formulated

generic construction of binary sequences of period 2n with optimal odd correlation magnitude based on quaternary sequences of odd period n binary sequences with low odd correlation have important applications in communication systems to reduce interference in this paper using the interleaving technique we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation as a result some new binary sequences with optimal odd auto correlation magnitude are obtained besides two sets consisting of 2 n 1 binary sequences of period 2 2 n 1 with the maximum odd correlation magnitude 2 n 1 2 2 are derived which are the first two optimal classes of binary sequence sets achieving the sarwate bound on the odd correlation magnitude in the literature

on a class of elliptic problems in r symmetry and uniqueness results in the plane r 2 we classify all solutions for an elliptic problem of liouville type involving a radial weight function as a consequence we clarify the origin of the non radially symmetric solutions for the given problem as established by chanillo and kiessling for a more general class of liouville type problems we show that rather than radial symmetry the solutions always inherit the invariance of the problem under inversion with respect to suitable circles this symmetry result is derived with the help of a shrinking sphere method

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

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

new binary sequences with optimal autocorrelation magnitude new binary sequences of period n 4 2m 1 for even m ges 4 are found where the sequences are described by a 4 x 2m 1 array structure the new sequences are almost balanced and have four valued autocorrelation i e n 0 plusmn4 which is optimal with respect to autocorrelation magnitude the complete autocorrelation distribution and the exact linear complexity of the sequences are mathematically derived finally it is shown that the sequences are implemented by a combination of linear feedback shift registers and a simple logic

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

a new family of almost difference sets and some necessary conditions almost difference sets have important applications in cryptography and coding theory in this paper new families of almost difference sets are constructed some necessary conditions for the existence of v k spl lambda t almost difference sets in z sub v are derived

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

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

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

on multivortices in the electroweak theory ii existence of bogomol nyi solutions in ℝ2 in this paper we study the bogomol nyi equations of the electroweak theory in the full plane we will show that for any distribution of the vortices there exists a two parameter family of gauge distinct solutions moreover we also establish some sharp decay rate estimates for these solutions

periods of interleaved and nonuniformly decimated sequences periods of interleaved and nonuniformly decimated integer sequences are analyzed a characterization of the period of an interleaved sequence in terms of the constituent periodic integer sequences is first derived this is then used to generalize the result of blakley and purdy 1981 on the period of a decimated integer sequence obtained by a periodic nonuniform decimation the technique developed and results may be interesting for analyzing the period of various pseudorandom sequences especially in stream cipher and spread spectrum applications

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

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

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

weighted barycentric sets and singular liouville equations on compact surfaces given a closed surface we prove a general existence result for some elliptic pde with exponential nonlinearities and negative dirac deltas extending a theory recently obtained for the regular case this is done by global methods since the associated euler functional might be unbounded from below we define a new model space generalizing the so called space of formal barycenters and characterizing up to homotopy equivalence its low sublevels as a result the analytic problem is reduced to a topological one concerning the contractibility of this model space to this aim we prove a new functional inequality in the spirit of chen and li 1991 11 and then employ a min max scheme based on conical construction jointly with the blow up analysis in bartolucci and montefusco 2007 4 after bartolucci and tarantello 2002 brezis and merle 1991 and this study is motivated by abelian chern simons theory in self dual regime or from the problem of prescribing the gaussian curvature with conical singularities generalizing a problem raised in kazdan and warner 1974 24

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

degree counting and shadow system for toda system of rank two one bubbling abstract we initiate the program for computing the leray schauder topological degree for toda systems of rank two this program still contains a lot of challenging problems for analysts as the first step we prove that if a sequence of solutions u 1 k u 2 k blows up then one of h j e u j k m h j e u j k d v g j 1 2 tends to a sum of dirac measures this is so called the phenomena of weak concentration our purposes in this article are i to introduce the shadow system due to the bubbling phenomena when one of parameters i crosses 4 and j 4 n where 1 i j 2 ii to show how to calculate the topological degree of toda systems by computing the topological degree of the general shadow systems iii to calculate the topological degree of the shadow system for one point blow up we believe that the degree counting formula for the shadow system would be useful in other problems

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

relationships between m sequences over gf q and gf q sup m it is shown that m sequences over gf q sup m of length q sup nm 1 corresponding to primitive polynomials in gf q sup m x of degree n can be generated from known m sequences over gf q of length q sup nm 1 obtained from primitive polynomials in gf q x of degree mn a procedure for generating the m sequences over gf q sup 2 from m sequences over gf q was given which enables the generation of m sequences over gf p sup 2n in addition it was shown that all of the primitive polynomials in gf q sup m x can be obtained from a complete set of the primitive polynomials in gf q x

degree counting for toda system with simple singularity one point blow up abstract in this paper we study the degree counting formula of the rank two toda system with simple singular source when 1 0 4 4 8 and 2 4 n the key step is to derive the degree formula of the shadow system which arises from the bubbling solutions as 1 tends to 4 in order to compute the topological degree of the shadow system we need to find some suitable deformation during this deformation we shall deal with new difficulty arising from the phenomenon blow up does not necessarily imply concentration of mass this phenomenon occurs due to the collapsing of singularities this is a continuation of the previous work 25

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

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

on a planar liouville type problem in the study of selfgravitating strings abstract motivated by the construction of selfgravitating strings cf yang 2001 1994 22 23 we analyze a liouville type equation on the plane derived in yang 1994 23 we establish sharp existence and uniqueness properties for the corresponding radial solutions we investigate also when the problem allows for non radial solutions

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 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

zonal local solution method for the turbulent navier stokes equations azonal local solution method is developed for the solution of the compressible navier stokes equations the main feature of the method is coupling of the navierstokes equations with the euler equations and the local mesh solution procedure mesh sequencing multilevel technique is also used for the improvement of the efficiency of the algorithm the methodology is applied to turbulent flowfields past an airfoil a flux vector splitting method with an upwind scheme up to fourth order accuracy is used for the discretization of the inviscid fluxes the system of the equations is solved by an unfactored implicit method using gauss seidel relaxation contents techological improvements in supercomputer speed and memory size provided the means to solve the full compressible navier stokes equations for turbulent flowfields and complex geometries however large amounts of computer time are required for the solution of the equations especially for problems in design practice to reduce the computational time a zonal local solution method is presented for the solution of the two dimensional navier stokes equations in high reynolds number flows the equations are solved in time dependent form and for a curvilinear body fitted coordinate system jut gvis r 1 where is the jacobian of the transformation of the cartesian coordinates x z to curvilinear coordinates f the subscripts inv vis indicate the inviscid and viscous fluxes respectively and u is the conservative variables matrix the equations are solved by a finite volume navier stokes code1 which uses a modified 1 steger warming flux vector splitting fvs method for the discretization of the inviscid fluxes the fvs method split the fluxes into two parts positive and negative in accordance with the sign of the eigenvalues 2

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

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

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

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

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

two dimensional euler flows with concentrated vorticities for a planar model of euler flows proposed by tur and yanovsky 2004 we construct a family of velocity fields w e for a fluid in a bounded region with concentrated vorticities e for e 0 small more precisely given a positive integer and a sufficiently small complex number a we find a family of stream functions e which solve the liouville equation with dirac mass source e e 2 e e 4 pa e in e 0 on for a suitable point p p a e the vorticities e e concentrate in the sense that 1 e 4 pa e 8 1 j 1 pa e a j 0 as e 0 j 1 where the satellites a 1 a 1 denote the complex 1 roots of a the point p a e lies close to a zero point of a vector field explicitly built upon derivatives of order 1 of the regular part of green s function of the domain

on the linear complexity of binary sequences of period 4n with optimal autocorrelation value magnitude three classes of binary sequences of period 4n with optimal autocorrelation value magnitude have been constructed by tang and gong based on interleaving certain kinds of sequences of period n i e the legendre sequence twin prime sequence and generalized gmw sequence in this paper by means of sequence polynomials of the underlying sequences the properties of roots of the corresponding sequence polynomials of the interleaved sequences with period 4n and optimal autocorrelation value magnitude are discussed in the splitting field of xn 1 as a consequence both the minimal polynomials and linear complexities of these three classes of sequences are completely determined except for the case of the sequences obtained from the generalized gmw sequences for the latter the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based on m sequences instead of generalized gmw sequences