a kind of helicoidal surfaces in 3 dimensional minkowski space abstract in this paper we constructed a helicoidal surface with a light like axis with prescribed mean curvature or gauss curvature given by smooth function in 3 dimensional minkowski space e 1 3 and solved an open problem left by beneki kaimakamis and papantoniou in j math anal appl 275 2002 586 614

large deviations of the lyapunov exponent and localization for the 1d anderson model the proof of anderson localization for the 1d anderson model with arbitrary e g bernoulli disorder originally given by carmona klein martinelli in 1987 is based in part on the multi scale analysis later in the 90s it was realized that for one dimensional models with positive lyapunov exponents some parts of multi scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle leading to nonperturbative proofs for 1d quasiperiodic models in this paper we present a short proof along these lines for the anderson model to prove dynamical localization we also develop a uniform version of craig simon s bound that works in high generality and may be of independent interest

on spacelike hypersurfaces with constant mean curvature in the de sitter space soit n n n 1 c g une variete de lorentz a n 1 dimensions de courbure constante positive c soit m une hypersurface du genre espace complete a courbure moyenne constante h dans n on suppose que 1 h c 1 2 quand n 2 2 h 2 n 1 c 1 2 n quand n 3 alors m est totalement ombilicale

regularity of the invariant measure and of the density of states in the one dimensional anderson model abstract let h 1 2 v on l2 z where v x x z are i i d r v s with common probability distribution let h t e itvd v let n e be the integrated density of states and let e be the invariant measure at energy e it is proven 1 1 let h be d times differentiable on 0 with bounded derivatives such that h j t 0 as t for j 0 1 d then i n e is a cd function ii if d 3 e is absolutely continuous for all e r and d e dx is of class c d 1 2 1 jointly in e and x 2 2 let h be differentiable on 0 with h j t o e b t for j 0 1 and some b 0 then d e dx is jointly analytic in e and x

de bruijn sequences adjacency graphs and cyclotomy we study the problem of constructing de bruijn sequences by joining cycles of linear feedback shift registers lfsrs with reducible characteristic polynomials the main difficulty for joining cycles is to find the location of conjugate pairs between cycles and the distribution of conjugate pairs in cycles is defined to be adjacency graphs let l x be a characteristic polynomial and l x l 1 x l 2 x cdots l r x be a decomposition of l x into pairwise co prime factors first we show a connection between the adjacency graph of mathrm fsr l x and the association graphs of mathrm fsr l i x 1 leq i leq r by this connection the problem of determining the adjacency graph of mathrm fsr l x is decomposed to the problem of determining the association graphs of mathrm fsr l i x 1 leq i leq r which is much easier to handle then we study the association graphs of lfsrs with irreducible characteristic polynomials and give a relationship between these association graphs and the cyclotomic numbers over finite fields at last as an application of these results we explicitly determine the adjacency graphs of some lfsrs and show that our results cover the previous ones

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

simple and robust binary self location patterns a simple method to generate a 2 d binary grid pattern which allows for absolute and accurate self location in a finite planar region is proposed the pattern encodes position information in a local way so that reading a small number of its black or white pixels at any place provides sufficient data from which the location can be decoded both efficiently and robustly

invariant conformal metrics on ⁿ in this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the eigenvalues of its schouten tensor also we study conformal metrics on the sphere which are invariant by a k parameter subgroup of conformal diffeomorphisms of the sphere giving a bound on its maximum dimension moreover we classify conformal metrics on the sphere whose eigenvalues of the shouten tensor are all constant we call them isoparametric conformal metrics and we use a clas

harmonic analysis on sl 2 r and smoothness of the density of states in the one dimensional anderson model we consider infinite jacobi matrices with ones off diagonal and independent identically distributed random variables with distributionf v dv on diagonal iff has compact support and lies in some sobolev spacel 1 then we prove that the integrated density of states k e isc ine

n dimensional area of minimal rotational hypersurfaces in spheres abstract let m r n denote the set of compact minimal rotational hypersurfaces in the n 1 dimensional sphere s n 1 for any compact hypersurface m s n 1 let us denote by m its n dimensional area in this paper we show that for any integer n 2 the set of numbers a n m m m r n is a discrete set we also show that if m m r 3 then either m s 3 or m m 0 3 or m m 0 3 where m 0 n s n 1 n 1 n s 1 1 n finally for 2 n 100 we show numerically evidence that if m m r n then either m s n or m m 0 n or m 2 m 0 n we strongly believe that for any m m r n either m s n or m m 0 n or m 2 m 0 n for all n

the adjacency graphs of lfsrs with primitive like characteristic polynomials we consider the adjacency graphs of the linear feedback shift registers lfsrs with characteristic polynomials of the form l x p x where l x is a polynomial of small degree and p x is a primitive polynomial it is shown that their adjacency graphs are closely related to the association graph of l x and the cyclotomic numbers over finite fields by using this connection we give a unified method to determine their adjacency graphs as an application of the method we explicitly calculate the adjacency graphs of lfsrs with the characteristic polynomials of the form 1 x x 3 x 4 p x and construct a large class of de bruijn sequences from them

constructions for perfect maps and pseudorandom arrays a construction of perfect maps i e periodic r v binary arrays in which each n m binary matrix appears exactly once is given a similar construction leads to arrays in which only the zero n m matrix does not appear and to a construction in which only a few n m binary matrices do not appear a generalization to the nonbinary case is given the constructions involve an interesting problem in shift register theory the solution is given for almost all the case of this problem

flat surfaces in the hyperbolic 3 space in this paper we give a conformal representation of flat surfaces in the hyperbolic 3 space using the complex structure induced by its second fundamental form we also study some examples and the behaviour at infinity of complete flat ends

an efficient algorithm for the generation of debruijn cycles an algorithm is presented for the generation of binary debruijn sequences using feedback shift registers fsrs the algorithm is based on the principle of cycle joining through which all the cycles in the cycle structure of a fsr can be joined together to one complete cycle thereby producing a debruijn sequence of period 2 sup n where n is the length of the fsr by a proper choice of the feedback function of the fsr o 2 sup 2n sup log2n debruijn sequences of period 2 sup n can be generated requiring only 3n bits of storage and at most 4n fsr shifts for the generation of the next bit in the sequence

minimal immersions into space forms with two principal curvatures in 2 chern do carmo and kobayashi consider minimal immersions of an ndimensional manifold m into the unit sphere s n of the n n l dimensional euclidean space ir n n l with the property that the second fundamental form has constant length n 2 1 n if m is compact this is the smallest possible value for a non totally geodesic minimal immersion as above they prove that locally m is either a piece of a veronese surface n 2 n 2 or the product of two spaces of dimensions m and n m and of constant curvatures n m and n n m they also prove the corresponding global result under a compactness assumption for m the main feature of the situation is that the second fundamental form in any normal direction has two distinct eigenvalues and in general the respective eigenspaces will determine involutive distributions whose integral manifolds will give the local product structure this leads naturally to the study of minimal immersions into spaces of constant curvature such that the second fundamental form has in any normal direction at most two distinct eigenvalues this problem was studied by otsuki in 9 for the case of hypersurfaces he proves the following result see also remark 3 7

on information rates of the fading wyner cellular model via the thouless formula for the strip in this paper we apply the theory of random schrodinger operators to the analysis of multiusers communication channels similar to the wyner model which are characterized by short range intercell interference with h the channel transfer matrix hhf is a narrow band matrix a fact that does not permit the use of classical random matrices theory on the other hand hhf is in many aspects similar to a random schrodinger operator we relate the per cell sum rate capacity of the channel to the integrated density of states of a random schrodinger operator the latter is then related to the top lyapunov exponent of a random sequence of matrices via a version of the thouless formula we also derive several bounds on the limiting per cell sum rate capacity some based on the theory of random schrodinger operators and some derived from information theoretical considerations finally we get explicit results in the high signal to noise ratio snr regime for some particular cases

the properties of a class of linear fsrs and their applications to the construction of nonlinear fsrs in this paper the cycle structure and adjacency graphs of a class of linear feedback shift registers lfsrs are determined by recursively applying the d morphism to the maximum length lfsrs and representing the cycles by generating functions a new family of maximum length nonlinear feedback shift registers nfsrs are proposed based on the properties of these lfsrs the number of nfsrs in the proposed family is also considered

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

critical curves for a santalo problem in 3 space forms abstract l santalo 1956 studied in 15 the minimization of frenet first curvature dependent energies for spaces of curves constrained to lie in a surface of the euclidean 3 space in this paper we analyze an extension of that problem by considering energy functionals determined by lagrangians which depend not only on the curvature but also on the torsion acting on spaces of surface contained clamped curves of real 3 space forms

shannon theoretic approach to a gaussian cellular multiple access channel with fading shannon theoretic limits on the achievable throughput for a simple infinite cellular multiple access channel mac model wyner 1994 in the presence of fading are presented in this model which is modified to account for flat fading the received signal at a given cell site s antenna is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor spl alpha spl isin 0 1 times the sum of the faded signals received from the adjacent cells accompanied by gaussian additive noise this model serves as a tractable model providing considerable insight into complex and analytically intractable real world cellular communications both linear and planar cellular arrays are considered with exactly k active users in each cell we assume a hyper receiver jointly decoding all of the users incorporating the received signals from all of the active cell sites the hyper receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system in this work we consider the intracell time division multiple access tdma and the wideband wb protocols we focus on the maximum reliably transmitted equal rate bounds to this rate are found for the intracell tdma protocol by incorporating information theoretic inequalities and the chebyshev markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices we demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a rayleigh distribution i e rayleigh fading for this special case we observe the rather surprising result that fading may increase the maximum equal rate for a certain range of spl alpha as compared to the nonfaded case in this setting the wb strategy which achieves the maximum reliable equal rate of the model is proved to be superior to the tdma scheme an upper bound to the maximum equal rate of the wb scheme is also obtained this bound is asymptotically tight when the number of users is large k spl gt 1 the asymptotic bound shows that the maximum equal rate of the wb scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor spl alpha spl isin 0 1 signal to noise ratio snr values this result is found to be independent of the statistics of the fading coefficients

conformal hypersurfaces with the same gauss map in this paper we provide a complete classification of all hypersurfaces of euclidean space which admit conformal deformations other than the ones obtained through conformal diffeomorphisms of the ambient space preserving the gauss map elie cartan in one of his earlier papers in differential geometry classified all euclidean hypersurfaces of dimension at least five which admit conformal deformations other than the trivial ones obtained through compositions with conformal diffeomorphisms of the ambient space when all possible conformal deformations are trivial a hypersurface is called conformally rigid first cartan proved that a hypersurface is conformally rigid if at no point does there exist a principal curvature of multiplicity at least n 2 see ca cd2 or da using this he concluded that a conformally deformable hypersurface is either conformally flat or a 2 parameter envelope of spheres or planes of some very special type moreover the set of all conformal deformations is either a 1parameter family or there is just one other deformation in this paper we classify all euclidean hypersurfaces which admit nontrivial conformal deformations preserving the gauss map in the isometric case a complete classification for any codimension has been obtained by dajczer and gromoll dg2 while the conformal case but only for surfaces is due to vergasta ve2 theorem let f g mn rn 1 n 3 be conformal immersions of an ndimensional connected riemannian manifold with the same gauss map assume that on no open subset do they differ by a conformal diffeomorphism of rn l then f mn is part of one of the following examples while g mn is of the same type i a minimal real kaehler hypersurface ii a rotation hypersurface over a plane curve iii a rotation hypersurface over a minimal surface in r3 minimal real kaehler hypersurfaces have been completely classified by dajczer and gromoll in dg2 the assumption that f and g do not differ locally by a conformal deformation of the ambient space has been introduced in order to produce a global result without that assumption our proof shows that the only other possibility is to have an open subset where up to homothety received by the editors december 10 1993 1991 mathematics subject classification primary 53c42 1995 american mathematical society

constant mean curvature invariant surfaces and extremals of curvature energies abstract we determine the extremal curves of curvature energy functionals which generalize a variational problem studied by blaschke in r 3 the generalization is made by extending both the lagrangian energy itself and the ambient space to riemannian and lorentzian 3 space forms then we show that constant mean curvature cmc invariant surfaces in 3 space forms can be constructed locally as the evolution of the above extremals under their binormal flow with appropriate velocity moreover we see that these surfaces are intrinsically described by a warping function satisfying an ermakov milne pinney equation finally we use the previous findings to extend known results on isometric deformations of cmc surfaces and the lawson s correspondence of cmc cousins to our background spaces

rigidity theorems on smooth metric measure spaces with weighted poincare inequality we obtain some results on the rigidity of complete smooth metric measure spaces with weighted poincare inequality which generalize previous results in cheng and zhou 2009 dung 2012 dung and sung 2013 fu and li 2010 fu and yang 2012 lam 2010 li 2005 li and wang 2001 2006 wang 2012 as an application we prove that a complete n 1 2n2 stable minimal hypersurface in rn 1 with n 3 must have only one end

algorithms for the generation of full length shift register sequences two algorithms are presented for the generation of full length shift register cycles also referred to as de bruijn sequences the first algorithm generates 2 k cdot g n k full cycles of length 2 n using 3n k cdot g n k bits of storage where k is a free parameter in the range 1 leq k leq 2 n 4 2 and g n k is of the order of n 2 log k the second algorithm generates about 2 n 2 4 full cycles of length 2 n using about n 2 2 bits of storage in both algorithms the time required to produce the next bit from the last n bits is close to n a possible application to the construction of stream ciphers is indicated

dynamical description of bidimensional linear systems with a measurable 2 sheet abstract the dynamical behaviour of the projective flow induced by a family of bidimensional linear systems with a measurable 2 sheet is studied when the lyapunov exponent vanishes it is shown that the trajectories move from one sheet to the other either whenttends to or this extends and completes some known results on oscillatory dynamics to a more general ergodic situation

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

franco american meeting on the mathematics of random and almost periodic potentials we present the abstracts of papers given at a conference held at the ecole polytechnique in june 1983 on the mathematics of random and almost periodic potentials

rotation hypersurfaces in spaces of constant curvature rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed a local characterization of such hypersurfaces with dimensions greater than two is given in terms of principal curvatures some special cases of rotation hypersurfaces with constant mean curvature in hyperbolic space are studied in particular it is shown that the well known conjugation between the helicoid and the catenoid in euclidean three space extends naturally to hyperbolic three space h3 in the latter case catenoids are of three different types and the explicit correspondence is given it is also shown that there exists a family of simply connected complete embedded nontotally geodesic stable minimal surfaces in h3

extremal curves for weighted elastic energy in surfaces of 3 space forms a variational problem closely related to the bending energy of curves contained is surfaces of real 3 space forms is considered we seek curves in a surface which are critical for the elastic energy when this is weighted by the total squared normal curvature energy under two different sets of constraints clamped curves and one free end curves of constant length we start by deriving the first variation formula and the corresponding euler lagrange equations and natural boundary conditions of these energies and characterize critical geodesics we show how surfaces locally foliated by critical geodesics can be found by using the fundamental theorem of submanifolds in order to find explicit solutions we classify complete rotation surfaces in a real space form for which every parallel is critical

a class of de bruijn sequences in this paper a class of linear feedback shift registers lfsrs with characteristic polynomial 1 x 3 p x is discussed where p x is a primitive polynomial of degree n 2 the cycle structure and adjacency graphs of the lfsrs are determined a new class of de bruijn sequences is constructed from these lfsrs and the number of de bruijn sequences in the class is also considered to illustrate the efficiency of constructing de bruijn sequences from these lfsrs an algorithm for producing some corresponding maximum length nonlinear feedback shift registers with time and memory complexity o n is also proposed

capacity and power scaling laws for finite antenna mimo amplify and forward relay networks in this paper we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple input multiple output d times d antenna amplify and forward relay networks in particular we model these networks as random dynamical systems and calculate their d lyapunov exponents our analysis can be applied to systems with any per hop channel fading distribution although in this contribution we focus on rayleigh fading our main results are twofold 1 the total transmit power at the n th node will follow a deterministic trajectory through the network governed by the network s maximum lyapunov exponent and 2 the capacity of the i th eigenchannel at the n th node will follow a deterministic trajectory through the network governed by the network s i th lyapunov exponent before concluding we concentrate on some applications of our results in particular we show how the lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other and how this relates to the amplification strategy and the number of antennas at each relay we also use them to determine the extra cost in power associated with each extra multiplexed data stream

anderson localization for the almost mathieu equation ii point spectrum for lambda 2 we prove that for any 2 and a e the pure point spectrum of the almost mathieu operator h n n 1 n 1 cos 2 n n contains the essential closure hat sigma of the spectrum corresponding eigenfunctions decay exponentially the singular continuous component if it exists is concentrated on a set of zero measure which is nowhere dense in hat sigma

log holder continuity of the integrated density of states for stochastic jacobi matrices we consider the integrated density of states k e of a general operator on l2 v of the formh h0 v where h 0 u n sum limits left i right 1 u n i and vu n v n u n wherev is a general bounded ergodic stationary process on v we show that k e k e c log e e 1 when e e 1 2 the key is a thouless formula for the strip

eigenvalue estimates for minimal surfaces in hyperbolic space this paper gives an upper bound for the first eigenvalue of the universal cover of a complete stable minimal surface in hyperbolic space and a sharper one for least area disks

a scalable method for constructing galois nlfsrs with period 2 n 1 using cross join pairs a method for constructing n stage galois nlfsrs with period 2n 1 from n stage maximum length lfsrs is presented nonlinearity is introduced into state cycles by adding a nonlinear boolean function to the feedback polynomial of the lfsr each assignment of variables for which this function evaluates to 1 acts as a crossing point for the lfsr state cycle the effect of nonlinearity is cancelled and state cycles are joined back by adding a copy of the same function to a later stage of the register the presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on cross join pairs it is feasible for large n

limit periodic schrodinger operators in the regime of positive lyapunov exponents abstract we investigate the spectral properties of discrete one dimensional schrodinger operators whose potentials are generated by continuous sampling along the orbits of a minimal translation of a cantor group we show that for given cantor group and minimal translation there is a dense set of continuous sampling functions such that the spectrum of the associated operators has zero hausdorff dimension and all spectral measures are purely singular continuous the associated lyapunov exponent is a continuous strictly positive function of the energy it is possible to include a coupling constant in the model and these results then hold for every non zero value of the coupling constant

stochastic schrodinger operators and jacobi matrices on the strip we discuss stochastic schrodinger operators and jacobi matrices with wave functions taking values in l so there are 2l lyaponov exponents 1 l 0 l 1 2l 1 our results include the fact that if 1 0 on a set positive measure thenv is deterministic and one that says that e exactly 2j s are zero is the essential support of the a c spectrum of multiplicity 2j

metal insulator transition for the almost mathieu operator we prove that for diophantine and almost every the almost mathieu operator h n n 1 ni 1 cos 2 n n exhibits localization for 2 and purely absolutely continuous spectrum for 2

a successor rule framework for constructing k ary de bruijn sequences and universal cycles we present a simple framework for constructing k ary de bruijn sequences and more generally universal cycles via successor rules the framework is based on the often used method of joining disjoint cycles it generalizes several previously known de bruijn sequence constructions based on the pure cycling register and is applied to derive a new construction that is perhaps the simplest of all successors furthermore it generalizes an algorithm to construct binary de bruijn sequences based on any arbitrary nonsingular feedback function the framework is applied to derive and prove the correctness of successors to efficiently construct 1 universal cycles for k ary strings of length n whose weight is bounded by some w and 2 universal cycles for permutations it has also been subsequently applied to find the first universal cycle constructions for weak orders

clues to the hidden nature of de bruijn sequences abstract order n de bruijn sequences are the period 2 n binary sequences produced by an n stage feedback shift register theoretical results are summarized and data are presented for feedback functions generator polynomials linear spans and autocorrelation properties of modified de bruijn sequences

j simons type integral formula for hypersurfaces in a unit sphere abstract in this paper by investigating compact rotational hypersurfaces m n in a unit sphere s n 1 1 we get some integral formulas and then apply the integral formulas to characterize torus s 1 k n s n 1 n k n

mutual information of wireless channels and block jacobi ergodic operators shannon s mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver from this viewpoint the channel can also be represented by an ergodic self adjoint block jacobi operator which is close in many aspects to a block version of a random schrodinger operator the mutual information is then related to the so called density of states of this operator in this paper it is shown that under the weakest assumptions on the channel the mutual information can be expressed in terms of a matrix valued stochastic process coupled with the channel process this allows numerical approximations of the mutual information in this general setting moreover assuming further that the channel coefficient process is a markov process a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related markov process this generalizes previous results from levy et al it is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime

embedded constant mean curvature tori in the three sphere we prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric and use this to give a complete classification of such surfaces for any given value of the mean curvature

on certain large random hermitian jacobi matrices with applications to wireless communications in this paper we study the spectrum of certain large random hermitian jacobi matrices these matrices are known to describe certain communication setups in particular we are interested in an uplink cellular channel which models mobile users experiencing a soft handoff situation under joint multicell decoding considering rather general fading statistics we provide a closed form expression for the per cell sum rate of this channel in high signal to noise ratio snr when an intra cell time division multiple access tdma protocol is employed since the matrices of interest are tridiagonal their eigenvectors can be considered as sequences with second order linear recurrence therefore the problem is reduced to the study of the exponential growth of products of two by two matrices for the case where k users are simultaneously active in each cell we obtain a series of lower and upper bound on the high snr power offset of the per cell sum rate which are considerably tighter than previously known bounds

complete minimal hypersurfaces in the hyperbolic space mathbb h 4 with vanishing gauss kronecker curvature we investigate 3 dimensional complete minimal hypersurfaces in the hyperbolic space h 4 with gauss kronecker curvature identically zero more precisely we give a classification of complete minimal hypersurfaces with gauss kronecker curvature identically zero a nowhere vanishing second fundamental form and a scalar curvature bounded from below

construction of de bruijn sequences from lfsrs with reducible characteristic polynomials in this paper a family of new de bruijn sequences is proposed through the construction of maximum length nonlinear feedback shift registers nfsrs let k be a positive integer and p 0 x p 1 x ldots p k x be the primitive polynomials in mathbb f 2 x with their degrees strictly increasing and pairwise coprime we determine the cycle structure and adjacency graphs of linear feedback shift registers lfsrs with characteristic polynomial q x prod nolimits i 0 k p i x in the case that p 0 x 1 x an algorithm is proposed to produce maximum length nfsrs from these lfsrs and it is shown that the algorithm can generate o 2 2 k 1 n n stage maximum length nfsrs with memory complexity o 2 k kn and time complexity o 2 n d k kn where n and d k are the degrees of q x and p k x respectively finally we illustrate the proposed algorithm in the case of k 2 in this case we prove that for any integer n geq 8 the algorithm can produce n stage maximum length nfsrs with time complexity as low as o n rm log log n

loi des grands nombres et perturbations pour des produits reductibles de matrices aleatoires independantes soit x x n n 1 une suite de matrices aleatoires reelles d d independantes de meme loi on etudie le comportement asymptotique de la suite 1 n log x n x 1 x n

rotational surfaces of constant astigmatism in space forms abstract a surface in a riemannian space is called surface of constant astigmatism if the difference between the principal radii of curvature at each point is a constant function in this paper we give a classification of all rotational surfaces of constant astigmatism in space forms we also prove that generating curves of such surfaces are critical points of a variational problem for a curvature energy using the description of these curves we locally construct all rotational surfaces of constant astigmatism as the associated binormal evolution surfaces from the generating curves

critical curves for the total normal curvature in surfaces of 3 dimensional space forms abstract a variational problem closely related to the bending energy of curves contained in surfaces of real 3 dimensional space forms is considered we seek curves in a surface which are critical for the total normal curvature energy and its generalizations we start by deriving the first variation formula and the corresponding euler lagrange equations of these energies and apply them to study critical special curves geodesics asymptotic lines lines of curvature on surfaces then we show that a rotation surface in a real space form for which every parallel is a critical curve must be a special type of a linear weingarten surface finally we give some classification and existence results for this family of rotation surfaces

disordered quantum walks in one lattice dimension we study a spin 12 particle moving on a one dimensional lattice subject to disorder induced by a random space dependent quantum coin the discrete time evolution is given by a family of random unitary quantum walk operators where the shift operation is assumed to be deterministic each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices we derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization put differently the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance our findings imply that this effect takes place if the coin is chosen at random from the haar measure or some measure continuous with respect to it but also for a class of discrete probability measures which support consists of two coins one of them being the hadamard coin

one dimensional schrodinger operators with random or deterministic potentials new spectral types abstract we prove sufficient conditions involving only potential asymptotic near one of the infinities in order to have purely absolutely continuous components in the spectrum these deterministic results are then applied to random cases and exhibit classes of models for which with probability one one component of the spectrum is purely absolutely continuous and the rest is dense pure point with exponentially decaying eigenfunctions

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

nontrivial minimal surfaces in a class of finsler spheres of vanishing s curvature abstract the minimal surface theory in finsler geometry deserves to be well developed as that in riemannian geometry in this paper we derive the mean curvature of submanifolds in a general manifold by considering the busemann hausdorff measure and holmes thompson measure respectively we then study the rotationally invariant minimal surfaces in the finsler 3 sphere endowed with an metric f k k k k k 1 where is a smooth function s 3 k is the berger sphere e 4 k 1 and k is a killing one form of constant length along the hopf fibers of s 3 we define the energy of the minimal surfaces and by using the volume ratio function introduced by the author and y b shen we give the explicit local expressions of the rotationally invariant bh minimal and ht minimal surfaces in such sphere respectively as a special case we give a detailed study of the rotationally invariant ht minimal surfaces in the 3 sphere with square metric

inverse problem for polynomials orthogonal on the unit circle polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated it is shown that the coefficients are in fact quasi periodic the measures associated with these quasi periodic coefficients are exhibited and necessary and sufficient conditions relating quasi periodicity and spectral measures of this type are given analogs for polynomials orthogonal on subsets of the real line are also presented

constructions of snake in the box codes for rank modulation snake in the box code is a gray code which is capable of detecting a single error gray codes are important in the context of the rank modulation scheme which was suggested recently for representing information in flash memories for a gray code in this scheme the codewords are permutations two consecutive codewords are obtained using the push to the top operation and distance measure is defined on permutations in this paper the kendall s metric is used as the distance measure we present a general method for constructing such gray codes we apply the method recursively to obtain a snake of length m2n 1 2n 1 2n 1 m2n 1 for permutations of s2n 1 from a snake of length m2n 1 for permutations of s2n 1 thus we have lim n m2n 1 s2n 1 0 4338 improving on the previous known ratio of lim n 1 n using the general method we also present a direct construction this direct construction is based on necklaces and it might yield snakes of length 2n 1 2 2n 1 for permutations of s2n 1 the direct construction was applied successfully for s7 and s9 and hence lim n m2n 1 s2n 1 0 4743