sinc interpolation of discrete periodic signals the paper introduces a method for the sinc interpolation of discrete periodic signals the convolution of the sinc kernel with the infinite sequence of a periodic function is rewritten as a finite summation the method is equivalent to trigonometrical interpolation by fourier series expansion

infinitesimal variation of hodge structures and the weak global torelli theorem for complete intersections in this paper we will study the weak global torelli theorem for complete intersections of hypersurfaces in a projective space let x be a non singular projective variety of dimension r with an ample line bundle l over the complex number field c then the primitive part hrm x z of the cohomology of x has a polarized hodge structure if the moduli space x of x exists we can define the global period map ho d r from the moduli space x to the classifying space d r of hodge structures attaching the point p in x to the hodge structure of the primitive part hrim xp z of the cohomology group of xp p e 4

variational torelli implies generic torelli david cox 1 ron donagi 2 and loring tu 3 1 department of mathematics amherst college amherst ma 01002 usa z department of mathematics northeastern university boston ma 02115 usa 3 department of mathematics tufts university medford ma 02155 usa introduction the methods of infinitesimal variation of hodge structure cf 3 provide a powerful tool for proving generic torelli theorems see 6 for the case of projective hypersurfaces however the success of this method depends on the implication variational torelli generic torelli in the literature various forms of this implication have appeared sometimes with proof cf 2 3 5 7 9 14 and 17 all previous precise formulations have required several auxiliary hypotheses including the existence of a coarse moduli space for the varieties in question the existence of a regular value for the period map i e a

picard numbers of surfaces in 3 dimensional weighted projective spaces in 7 steenbrink discusses the picard number of a generic quasismooth surface x in the weighted projective space p i 1 a b where gcd a b 1 his proof uses lefschetz pencils and is similar to lefschetz s classical proof for surfaces in ip 3 in this paper we will apply the methods of infinitesimal variation of hodge structure due to carlson et al 1 to generalize steenbrink s result to the case of arbitrary weights given the weighted projective space lp qo q q2 q3 it is customary to define

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

comments on sinc interpolation of discrete periodic signals in a recent paper by t schanze see ibid vol 43 p 1502 3 1995 the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation the expression obtained however is not numerically stable when evaluated at or near integer values of time this correspondence presents a numerically stable formulation that is equivalent to the results reported in the above cited paper and that when sampled is also shown to be equivalent to the inverse discrete fourier transform idft

a torelli theorem for simply connected elliptic surfaces with a section and p_g geqslant 2 0 the purpose of this note is to announce some recent results on the period mapping for simply connected elliptic surfaces with a section and p 2 among other things we are able to prove the period mapping for such surfaces has degree one that is to say it is generically injective in the terminology of c g this is called the weak global torelli theorem in order to make a precise statement of our results we must introduce some notation

realizable ideal d c and c d conversions for band limited periodic signals and characterization of single carrier block transmission for a real band limited periodic signal there are reconstruction formulas that realize the ideal discrete to continuous d c conversion within one period of the signal however the previous results may not be suitable for general complex band limited periodic signals for complex band limited periodic signals in this paper we first propose the reconstruction formulas which lead to realizable forms of ideal d c conversion we then derive the correlation function of the interpolation pulse and this helps us construct a matched filter that can implement the exact sampling c d conversion of a complex band limited periodic signal when there exists noise in the sampling process comparing with the ideal impulse sampling the proposed c d conversion can maintain finite output noise variance the correlation function of the output noise is also given and the oversampling effect of noise is analyzed for a complex interpolation pulse in general we cannot decouple the ideal d c or c d conversion into two independent d c or c d conversions for the real and imaginary parts of the signal we also give the extended forms and decomposition forms of the proposed d c and c d conversions our results are applied to derive the ideal d c and c d conversions in the precoded orthogonal frequency division multiplexing pofdm system the resulted interpolation pulses are used to characterize the single carrier sc block transmission under the pofdm architecture we give characteristics that distinguish the sc block transmission from traditional sc transmission

periodic solutions of duffing s equations with superquadratic potential abstract this paper is devoted to the study of harmonic and subharmonic solutions for the second order scalar nonlinear duffing s equation x g x p t x x where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g x sign x as x among other results we prove the existence of infinitely many harmonic and subharmonic solutions of any order p p t and if the potential g x of g x satisfies certain conditions of superquadratic growth at the new existence results can be applied to situations in which the more classical superlinear growth condition g x x as x is not satisfied in this manner various preceding theorems are improved and sharpened see the introduction for more details proofs are based on a generalized version of the poincare birkhoff twist theorem due to w ding

precoded and vector ofdm robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems the performance of orthogonal frequency division multiplexing ofdm systems may be degraded when intersymbol interference isi channels have spectral nulls also when isi channels have many taps the data rate overhead due to the insertion of the cyclic prefix is high we first propose a precoded ofdm system that may improve the performance of the ofdm systems for spectral null channels we also propose size k spl times x1 vector ofdm vofdm systems that reduce the cyclic prefix length by k times compared to the conventional ofdm systems the precoding scheme is simply to insert one or more zeros between each two sets of k consecutive information symbols although it can be generalized to a general form this precoding scheme may be able to remove the spectral nulls of an isi channel without knowing the isi channel when no zero is inserted between each two sets of k consecutive information symbols and only each k consecutive symbols are blocked together we obtain vofdm systems both theoretical performance analysis and simulation results are presented finally we compare the combination of the vofdm systems and the unitary matrix modulation with the conventional ofdm systems and the phase shift keying modulation where both differential noncoherent and coherent modulations and demodulations are considered

on the moduli space of pairs consisting of a cubic threefold and a hyperplane abstract we study the moduli space of pairs x h consisting of a cubic threefold x and a hyperplane h in p 4 the interest in this moduli comes from two sources the study of certain weighted hypersurfaces whose middle cohomology admit hodge structures of k3 type and on the other hand the study of the singularity o 16 the cone over a cubic surface in this paper we give a hodge theoretic construction of the moduli space of cubic pairs by relating x h to certain lattice polarized cubic fourfolds y a period map for the pairs x h is then defined using the periods of the cubic fourfolds y the main result is that the period map induces an isomorphism between a git model for the pairs x h and the baily borel compactification of some locally symmetric domain of type iv

extensions of the mountain pass theorem on considere une fonctionnelle c 1 i x r ou x est un espace de banach reel et ou i satisfait la condition de compacite de palais smale on presente une serie de theoremes qui generalisent le theoreme du col

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

notes on the interpolation of discrete periodic signals using sinc function related approaches considering the sinc interpolation of discrete periodic signals this correspondence establishes the equivalence of two recently published methods furthermore the interpolation methods are equivalent to a fractional delay filter designed using the frequency sampling technique a numerically stable and computationally attractive form of the equivalent methods is presented