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924
Endogenous lifetime and economic growth
 Journal of Economic Theory
, 2004
"... errors are mine. Endogenous Lifetime and Economic Growth Conventional wisdom attributes the severity of mortality in poorer countries to widespread poverty and inadequate living conditions. This paper considers the possibility that persistent poverty may arise, in turn, from a high incidence of mort ..."
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Cited by 129 (3 self)
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errors are mine. Endogenous Lifetime and Economic Growth Conventional wisdom attributes the severity of mortality in poorer countries to widespread poverty and inadequate living conditions. This paper considers the possibility that persistent poverty may arise, in turn, from a high incidence of mortality. Endogenous mortality risk is introduced in a twoperiod overlapping generations model: probability of survival from the ¯rst period to the next depends upon health capital that can be augmented through public investment. High mortality societies do not grow fast since shorter lifespans discourage saving and investment; multiple steadystates are possible. High mortality also reduces returns on investments, like education, where risks are undiversi¯able. When human capital drives economic growth, countries di®ering in only health capital do not converge to similar living standards; `threshold e®ects ' may also result.
NUMBER THEORETIC ALGORITHMS FOR ELLIPTIC CURVES
, 2008
"... We present new algorithms related to both theoretical and practical questions in the area of elliptic curves and class field theory. The dissertation has two main parts, as described below. Let O be an imaginary quadratic order of discriminant D < 0, and let K = Q ( √ D). The class polynomial HD ..."
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Cited by 1 (0 self)
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to compute HD modulo p for p inert which is used in the Chinese remainder theorem algorithm to compute HD. For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on the points of order n of E. The Weil pairing is a useful tool in both the theory of elliptic curvesand the application
Czechoslovak Mathematical Journal, 37 (112) 1987, Praha NATURAL TRANSFORMATIONS IN DIFFERENTIAL GEOMETRY
, 1985
"... The aim of tbis paper is to develop an efficient tool for handling natural transformations in differential geometry, like the foot point projection of the tangent bundle, the canonical flip mapping on the second tangent bundle, vertical lift and vertical projection, fibre addition and fibre multipli ..."
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multiplication. The natural setting for this is the study of product preserving (multiplicative) functors on the category Mf of smooth finite dimensional manifolds. We prove that (under some mild conditions) any such functor F is given by the action of a Weilalgebra A (see 1.6) on manifolds, in particular
acid dependent Gcn4p stability regulation occurs exclusively in the yeast nucleus.
"... An dieser Stelle möchte ich mich zunächst einmal gerne bei meinem ´Chef ´ Gerhard Braus bedanken. Nicht weil es sich so gehört, sondern weil ich in den letzten Jahren stets prima mit ihm klargekommen bin, es immer sehr lustig war, seinen glaubwürdigen und weniger glaubwürdigen Geschichten zuzuhören ..."
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An dieser Stelle möchte ich mich zunächst einmal gerne bei meinem ´Chef ´ Gerhard Braus bedanken. Nicht weil es sich so gehört, sondern weil ich in den letzten Jahren stets prima mit ihm klargekommen bin, es immer sehr lustig war, seinen glaubwürdigen und weniger glaubwürdigen Geschichten zuzuhören
Positive extensions, FejérRiesz factorization and autoregressive filters in two variables
 Ann. of Math
, 2004
"... In this paper we treat the twovariable positive extension problem for trigonometric polynomials where the extension is required to be the reciprocal of the absolute value squared of a stable polynomial. This problem may also be interpreted as an autoregressive filter design problem for bivariate st ..."
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Cited by 28 (11 self)
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In this paper we treat the twovariable positive extension problem for trigonometric polynomials where the extension is required to be the reciprocal of the absolute value squared of a stable polynomial. This problem may also be interpreted as an autoregressive filter design problem for bivariate stochastic processes. We show that the existence of a solution is equivalent to solving a finite positive definite matrix completion problem where the completion is required to satisfy an additional low rank condition. As a corollary of the main result a necessary and sufficient condition for the existence of a spectral FejérRiesz factorization of a strictly positive twovariable trigonometric polynomial is given in terms of the Fourier coefficients of its reciprocal. Tools in the proofs include a specific twovariable Kronecker theorem based on certain elements from algebraic geometry, as well as a twovariable ChristoffelDarboux like formula. The key ingredient is a matrix valued polynomial that appears in a parameterized version of the SchurCohn test for stability. The results also have consequences in the theory of twovariable orthogonal polynomials where a spectral matching result is obtained, as well as in the study of inverse formulas for doublyindexed Toeplitz matrices. Finally, numerical results are presented for both the autoregressive filter problem and the factorization problem. Key Words: autoregressive filter, bivariate stochastic processes, twovariable positive extension, structured matrix completions, doublyindexed Toeplitz matrix, twovariable
On the list and bounded distance decodability of the ReedSolomon codes
 In Proc. FOCS 2004
, 2004
"... For an errorcorrecting code and a distance bound, the list decoding problem is to compute all the codewords within a given distance to a received message. The bounded distance decoding problem is to find one codeword if there is at least one codeword within the given distance, or to output the empt ..."
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Cited by 24 (9 self)
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For an errorcorrecting code and a distance bound, the list decoding problem is to compute all the codewords within a given distance to a received message. The bounded distance decoding problem is to find one codeword if there is at least one codeword within the given distance, or to output the empty set if there is not. Obviously the bounded distance decoding problem is not as hard as the list decoding problem. For a ReedSolomon code [n, k]q, a simple counting argument shows that for any integer 0 < g < n, there exists at least one Hamming ball of radius n−g, which contains at least � � n g−k g /q many codewords. Let ˆg(n, k, q) be the smallest positive integer g such that � � n g−k g /q < 1. One knows that k ≤ ˆg(n, k, q) ≤ √ nk ≤ n. For the distance bound up to n − √ nk, it is well known that both the list and bounded distance decoding can be solved efficiently. For the distance bound between n − √ nk and n − ˆg(n, k, q), we do not know whether the ReedSolomon code is list, or bounded distance decodable, nor do we know whether there are polynomially many codewords in all balls of the radius. It is generally believed that the answers to both questions are no. There are public key cryptosystems proposed recently, whose security is based on the assumptions. In this paper, we prove: (1) List decoding can not be done for radius n − ˆg(n, k, q) or larger, otherwise the discrete logarithm over F q ˆg(n,k,q)−k is easy. (2) Let h and g be
LIFTS OF POINTS ON CURVES AND EXPONENTIAL SUMS. RÉGIS BLACHE
, 2003
"... Abstract. We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and give bounds for the degrees of their coordinate functions. Then we get bounds for exponential sums, exte ..."
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with coordinates in a padic field. The first result in this direction was the generalisation of the WeilCarlitzUchiyama bound. Let f ∈ Om[X] be a
Results 1  10
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924