weak solutions for an inviscid two phase flow model in physical vacuum abstract we investigate a free boundary problem for the inviscid two phase flow model with moving physical vacuum boundary which is a degenerate and characteristic hyperbolic system of conservation laws based on a suitable transformation a special degenerate parabolic approximation and delicate uniform energy estimates we prove the existence and uniqueness of the local weak solutions this can be regarded as a generalization of the results in coutand and shkoller 2011 5 from single phase gas model to two phase gas liquid model

time periodic solutions to the full navier stokes fourier system with radiation on the boundary the navier stokes fourier system is a well established model to describe motion of viscous compressible heat conducting fluids we study the existence of time periodic weak solutions and improve the result from 4 in the following sense we extend the class of pressure functions id est consider lower exponent and include also the effect of radiation on the boundary

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

a blow up criterion of strong solutions to a viscous liquid gas two phase flow model with vacuum in 3d abstract in this paper we get a blow up criterion for the strong solutions to the 3d viscous liquid gas two phase flow model with vacuum more precisely we prove that the bound of l t 1 l x norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions

time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces abstract consider the 3d incompressible boussinesq equations for rotating stably stratified fluids it is shown that this set of equations possesses a unique time periodic or almost time periodic solutions for external forces satisfying these properties which however do not necessarily need to be small an explicit bound on the size of the external force depending on the buoyancy frequency n is given which then allows for the unique existence of time periodic or almost periodic solutions in particular the size of the external forces can be taken large with respect to the buoyancy frequency the approach depends crucially on the dispersive effect of the rotation and the stable stratification

several new infinite families of bent functions and their duals bent functions are optimal combinatorial objects since their introduction substantial efforts have been directed toward their study in the last three decades a complete classification of bent functions is elusive and looks hopeless today therefore not only their characterization but also their generation are challenging problems this paper is devoted to the construction of bent functions first we provide several new effective constructions of bent functions self dual bent functions and antiself dual bent functions second we provide seven new infinite families of bent functions by explicitly calculating their dual

global well posedness of strong solutions to a two phase model with magnetic field for large oscillations in three dimensions abstract in this paper we consider cauchy problem for a two phase model with magnetic field in three dimensions under some smallness assumptions on the initial data but possibly large oscillations we obtain the global well posedness of strong solution as well as its large time behavior compared with wen and the first author s work 28 where global well posedness and large time behavior of strong solutions were obtained subject to smallness of initial data in h 2 norm we only need the smallness of initial energy which allows large oscillations of the initial data

time periodic solution for a 3 d compressible navier stokes system with an external force in r 3 abstract this paper is concerned with the existence of time periodic solutions of a compressible navier stokes system in the whole space r 3 with u 0 as x we first solve the problem in a sequence of bounded domains and letting the sequence tend to the original unbounded domain r 3 we obtain the existence of a strong small periodic solution as the limit of the corresponding sequence of solutions in the bounded domains

further results on generalized bent functions and their complete characterization this paper contributes to increase our knowledge on generalized bent functions including generalized bent boolean functions and generalized p ary bent functions with odd prime p by bringing new results on their characterization and construction in arbitrary characteristic more specifically we first investigate relations between generalized bent functions and bent functions by the decomposition of generalized bent functions this enables us to completely characterize generalized bent functions and mathbb z p k bent functions by some affine space associated with the generalized bent functions we also present the relationship between generalized bent boolean functions with an odd number of variables and generalized bent boolean functions with an even number of variables based on the well known maiorana mcfarland class of boolean functions we present some infinite classes of generalized bent boolean functions in addition we introduce a class of generalized hyperbent functions that can be seen as generalized dillon s ps functions finally we solve an open problem related to the description of the dual function of a weakly regular generalized bent boolean function with an odd number of variables via the walsh hadamard transform of their component functions and we generalize these results to the case of odd prime

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

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

stability of time periodic solution of the navier stokes equation on the half space under oscillatory moving boundary condition abstract navier stokes system on the half space with periodically oscillating boundary has a time periodic solution which depends on time variable and vertical variable only it is proved that the time periodic solution is asymptotically stable when the reynolds number is sufficiently small and the decay estimates of the perturbations are established in the frameworks of both strong and weak solutions

on the homology spectral sequence for topological hochschild homology marcel b6kstedt has computed the homotopy type of the topological hochschild homology of z p using his definition of topological hochschild homology for a functor with smash product here we show that easy conceptual proofs of his main technical result of are possible in the context of the homotopy theory of s algebras as introduced by elmendorf kriz mandell and may we give algebraic arguments based on naturality properties of the topological hochschild homology spectral sequence in the process we demonstrate the utility of the unstable lower notation for the dyer lashof algebra

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

systematic methods of constructing bent functions and 2 rotation symmetric bent functions in this paper we first present two systematic constructions of bent functions by modifying the truth tables of rothaus s bent function and maiorana mcfarland s bent function respectively the number of the newly constructed bent functions by modifying the truth table of rothaus s bent function is also determined the methods of constructing self dual bent functions are then given after the dual functions of these bent functions being determined finally as an application two constructions of 2 rotation symmetric bent functions are presented in this paper

algebraic k theory of topological k theory we are interested in the arithmetic of ring spectra to make sense of this we must work with structured ring spectra such as s algebras ekmm symmetric ring spectra hss or rings ly we will refer to these as salgebras the commutative objects are then commutative s algebras the category of rings is embedded in the category of s algebras by the eilenberg maclane functor r hr we may therefore view an s algebra as a generalization of a ring in the algebraic sense the added flexibility of s algebras provides room for new examples and constructions which may eventually also shed light upon the category of rings itself in algebraic number theory the arithmetic of the ring of integers in a number field is largely captured by its picard group its unit group and its brauer group these are

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

signal set design with constrained amplitude spectrum and specified time bandwidth product a new method for designing signals with a given time bandwidth product such that all the signals in the set have a flat amplitude spectrum and have low cross correlation function values is introduced it is shown that these signals lie on a signal parameter space ellipse for a given duration and bandwidth it is possible to trade off the cardinality of the set for better cross correlation properties between remaining members of the set proof that the cross correlation between these signals is bounded from above by a factor proportional to the square root of inverse distance between these signals along one of the axes of the ellipse is given it is also shown that the cross correlation between two signals that are furthest apart is bounded by the square root of inverse time bandwidth product of the signals in the set an example design is then given and a comparison of this signal set to some well known signal sets illustrates that it performs better when the metric is maximum cross correlation value the proposed signal set also has the advantage that it can be designed for any time bandwidth product instead of discrete values

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

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

systematic constructions of rotation symmetric bent functions 2 rotation symmetric bent functions and bent idempotent functions rotation symmetric bent functions and their generation two rotation symmetric bent functions are two classes of cryptographically significant boolean functions however few constructions have been presented in the literature which either have restriction on integer n or have algebraic degree no more than 4 in this paper for any even integer n ge 4 three classes of bent functions are presented respectively most notably the proposed n variable rotation symmetric bent functions and two rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to n 2 besides we obtain bent idempotent functions with the maximal algebraic degree n 2

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

existence and stability of time periodic solution to the compressible navier stokes equation for time periodic external force with symmetry abstract time periodic problem for the compressible navier stokes equation for barotropic flow on the whole space is studied the existence of a time periodic solution is proved for sufficiently small time periodic external force with some symmetry when the space dimension is greater than or equal to 3 the proof is based on the spectral properties of the time t map associated with the linearized problem around the motionless state with constant density in some weighted sobolev space the stability of the time periodic solution is also proved and the decay estimate of the perturbation is established

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

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

time periodic solution to a two phase model with magnetic field in a periodic domain abstract in the paper we consider a two phase model with magnetic field and a time periodic external force in a periodic domain in r n the existence of the time periodic solutions to the model is obtained by the topological degree theory and parabolic regularization method

weak solutions of a two phase navier stokes model with a general slip law abstract this work is devoted to a study of a gas liquid navier stokes model with a general slip law that allows the two phases to flow with unequal fluid velocity the slip law is general enough to describe counter current flow i e a situation where gas and liquid move in opposite direction motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p the slip law is incorporated in the mass and momentum equations resulting in a model where flow is described in terms of the gas velocity however the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity these new terms make the analysis challenging by carefully exploiting the positive external pressure p we are able to obtain uniform lower and upper bounds on a pressure related quantity this in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown

zero mach number limit for compressible flows with periodic boundary conditions we address the question of convergence to the incompressible navier stokes equations for slightly compressible viscous flows with ill prepared initial data and periodic boundary conditions the case of the whole space has been studied in an earlier paper by the author the functional setting is very close to the one used by h fujita and t kato for incompressible flows for arbitrarily large initial data we show that the compressible flow with small mach number exists as long as the incompressible one does in particular it exists globally if the corresponding incompressible solution exists for all time we further state a convergence result for the slightly compressible solution filtered by the group of acoustics introduction an engineer would hardly make a distinction between incom pressible flows and slightly compressible flows indeed incompressible navier stokes equations are usually regarded as an appropriate model for describing water in the present paper we study whether such an approximation is relevant from a mathematical viewpoint in the case of periodic boundary conditions the case of the whole space has been treated in 8 after some convenient rescaling see for instance the appendix of 16 or the introduction of 21 the equations for a slightly compressible fluid read

periodic solutions to the compressible magnetohydrodynamic equations in a periodic domain abstract in this paper we study the compressible magnetohydrodynamic system with a time periodic external force in a periodic domain in r n based on the idea in 12 we obtain the existence of a time periodic solution under some smallness and symmetry assumptions on the external force and improve the result from 12 in the following sense we extend the space dimension from 3 to n n 1 the uniqueness of the small periodic solution is also obtained

sheared algebra maps and operation bialgebras for mod 2 homology and cohomology the mod 2 steenrod algebraa and dyer lashof al gebra r have both striking similarities and dierences arising from their common origins in lower indexed algebraic operations these algebraic operations and their relations generate a bigraded bialgebrak whose module actions are equivalent to but quite dif ferent from those ofa andr the exact relationships emerge as sheared algebra bijections which also illuminate the role of the cohomology ofk as a bialgebra k has a particularly attractive and potentially useful structure providing a bridge between those ofa andr and suggesting possible applications to the miller spectral sequence and thea structure of dickson algebras

signal set design for band limited memoryless multiple access channels with soft decision demodulation signal sets are identified that maximize the cutoff rate region for a multiple access channel with an additive white gaussian noise in which the demodulator output alphabet is allowed to be infinite infinitely soft decisions the optimizing designs consist of a simplex signal set for each sender such that each sender s set is orthogonal to those of the other senders for second moment and for fractional out of band energy bandwidth constraints on the signals of each sender conditions are derived under which mutually orthogonal simplex sets are still optimal for the second moment constraint simplex sets derived from sinusoidal functions yield an optimal design and for the out of band energy constraint simplex sets derived from prolate spheroidal wave functions are optimal choices of signal sets that maximize the cutoff rate region for an additive shot noise limited multiple access optical channel subject to average energy and peak amplitude constraints are also identified

blow up criterion for 3d viscous liquid gas two phase flow model abstract this work deals with the blow up criterion for the strong solution to the three dimensional viscous liquid gas two phase flow model in terms of the l 1 0 t l norm of the gradient of the velocity with two types of boundary conditions the dirichlet boundary condition and the navier slip boundary condition there is no extra restriction on viscosity coefficients the result also applies to the whole space case

large time behavior for the system of a viscous liquid gas two phase flow model in r3 abstract the cauchy problem of a three dimensional compressible viscous liquid gas two phase flow model is considered in the present paper the global existence and uniqueness of solutions are established when the initial data is close to its equilibrium in the framework of sobolev space h 3 r 3 moreover the optimal l 2 l 2 convergence rates are also obtained for the solution

time periodic strong solutions to the incompressible navier stokes equations with external forces of non divergence form abstract we discuss the time periodic problem to the incompressible navier stokes equations on the whole space r n n 3 with the external forces of non divergence form firstly we consider the existence of time periodic solutions in b c r l n r n assuming the smallness of external forces in b c r l 1 r 3 and b c r l n 3 r n in the case n 4 next we show that the mild solution above becomes a strong solution in the topology of l n r n with a natural condition of the external force derived from the strong solvability of the inhomogeneous stokes equations in l n r n for this aim we re construct a strong solvability of an abstract evolution equation where the associated semigroup is not strongly continuous at t 0

cross correlation of p ary gmw sequences the cross correlation function of p ary p prime gmw sequences is investigated the well known m sequences are incorporated in these sequences gmw sequences also have the two level autocorrelation function but their linear span may be much larger than those of m sequences the calculation of the cross correlation function of gmw sequences is reduced to the cross correlation of the m sequences because many results on this kind of sequence are known in the literature only the cross correlation function of an m sequence with a gmw sequence has been known up to now

on the existence of square dot matrix patterns having a specific three valued periodic correlation function the author examines square matrices of size n containing dot patterns satisfying the following two restrictions 1 each column contain precisely one dot and 2 if the pattern is moved around over a plane tied by the same pattern when in all positions except the home position there is at most one overlap in dots from differing viewpoints there matrices are the characteristic functions of either a certain class of relative difference sets or else a select subset of bent functions also the existence of such an n n matrix implies the existence of a finite projective plane of order n a family of constructions for such matrices is available when n is prime a polynomial equation characterizing such matrices and resembling the hall polynomial equation of cyclic difference sets is presented analogs of known existence tests for cyclic difference sets are then applied to rule out existence for most nonprime values of n it is shown how such patterns can be used to provide hopping patterns for a frequency hopped multiple access system

topological hochschild homology of connective complex k theory let ku be the connective complex k theory spectrum completed at an odd prime p we present a computation of the mod p 1 homotopy algebra of the topological hochschild homology spectrum of ku