Real closed exponential fields

Paola D'Aquino; Julia F. Knight; Salma Kuhlmann; Karen Lange

Displaying similar documents to “Real closed exponential fields”

Exponential smoothing based on L-estimation

Přemysl Bejda, Tomáš Cipra (2015)

Kybernetika

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Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in $L_{1}$ are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data...

Decay of correlations for nonuniformly expanding systems

Sébastien Gouëzel (2006)

Bulletin de la Société Mathématique de France

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We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in $O (e^{- c \sqrt{n}})$ .

Exponential sums of the form $\sum χ {(x)}^{a x} ζ_{m}^{b x}$

S. Gurak (2007)

Acta Arithmetica

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The sum of digits of $⌊ n^{c} ⌋$

Johannes F. Morgenbesser (2011)

Acta Arithmetica

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Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2

Caroline Sweezy (2004)

Studia Mathematica

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For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and $S u ₁ \in L^{\infty} (S^{n - 1})$ then ${u ₁ |}_{S^{n - 1}} = f$ lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and $S u ₀ \in L^{\infty}$ implies ${u ₀ |}_{S^{n - 1}}$ is in the exponential square class; here S is the Lusin area integral. The exponential...

A proof of the valuation property and preparation theorem

Krzysztof Jan Nowak (2007)

Annales Polonici Mathematici

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The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded o-minimal theory T. The valuation property was conjectured by van den Dries, and proved for the polynomially bounded case by van den Dries-Speissegger and for the power bounded case by Tyne. Our proof uses the transfer principle for the theory $T_{c o n v}$ (i.e. T with an extra unary symbol denoting a proper convex subring), which-together with quantifier elimination-is due...

Exponential bounds for noncommuting systems of matrices

Brian Jefferies (2001)

Studia Mathematica

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It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form $| | e^{i ⟨ T, ζ ⟩} | | \leq C (1 + {| ζ |)}^{s} e^{r | ℑ ζ |}$ . The proof appeals to the monogenic functional calculus.

The single-point spectrum operators satisfying Ritt's resolvent condition

Yu. Lyubich (2001)

Studia Mathematica

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It is shown that an operator with the properties mentioned in the title does exist in the space $L_{p} (0, 1)$ , 1 ≤ p ≤ ∞. The maximal sector for the extended resolvent condition can be prescribed a priori jointly with the corresponding order of the exponential growth of the resolvent in the complementary sector.

Integral representations for solutions of exponential Gauß-Manin systems

Marco Hien, Céline Roucairol (2008)

Bulletin de la Société Mathématique de France

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Let $f, g : U \to 𝔸^{1}$ be two regular functions from the smooth affine complex variety $U$ to the affine line. The associated exponential Gauß-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system $𝒪_{U} e^{g}$ with respect to $f$ . We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

An Elementary Proof of the Exponential Conditioning of Real Vandermonde Matrices

Stefano Serra Capizzano (2007)

Bollettino dell'Unione Matematica Italiana

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We provide and discuss an elementary proof of the exponential con- ditioning of real Vandermonde matrices which can be easily given in undergraduate courses: we exclusively use the definition of conditioning and the sup-norm formula on $[-1,1]$ for Chebyshev polynomials of first kind. The same proof idea works virtually unchanged for the famous Hilbert matrix.

The zeros of functions of finite order in $C^{n}$

Lawrence Gruman (1983)

Annales Polonici Mathematici

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A note on the exponential Diophantine equation ${(4 m ² + 1)}^{x} + {(5 m ² - 1)}^{y} = {(3 m)}^{z}$

Jianping Wang, Tingting Wang, Wenpeng Zhang (2015)

Colloquium Mathematicae

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Let m be a positive integer. Using an upper bound for the solutions of generalized Ramanujan-Nagell equations given by Y. Bugeaud and T. N. Shorey, we prove that if 3 ∤ m, then the equation ${(4 m ² + 1)}^{x} + {(5 m ² - 1)}^{y} = {(3 m)}^{z}$ has only the positive integer solution (x,y,z) = (1,1,2).

Torsion points on curves and common divisors of $a^{k} - 1$ and $b^{k} - 1$

Nir Ailon, Zéev Rudnick (2004)

Acta Arithmetica

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Decay estimates of solutions of a nonlinearly damped semilinear wave equation

Aissa Guesmia, Salim A. Messaoudi (2005)

Annales Polonici Mathematici

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We consider an initial boundary value problem for the equation $u_{t t} - Δ u - \nabla ϕ \cdot \nabla u + f (u) + g (u_{t}) = 0$ . We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.

Prime numbers along Rudin–Shapiro sequences

Christian Mauduit, Joël Rivat (2015)

Journal of the European Mathematical Society

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For a large class of digital functions $f$ , we estimate the sums $\sum_{n \leq x} Λ (n) f (n)$ (and $\sum_{n \leq x} μ (n) f (n)$ , where $Λ$ denotes the von Mangoldt function (and $μ$ the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.

On The Exponential Properties Of The Implication

M. Stojaković (1972)

Publications de l'Institut Mathématique

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On Dirichlet-Schrödinger operators with strong potentials

Gabriele Grillo (1995)

Studia Mathematica

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We consider Schrödinger operators H = -Δ/2 + V (V≥0 and locally bounded) with Dirichlet boundary conditions, on any open and connected subdomain $D \subset ℝ^{n}$ which either is bounded or satisfies the condition $d (x, D^{c}) \to 0$ as |x| → ∞. We prove exponential decay at the boundary of all the eigenfunctions of H whenever V diverges sufficiently fast at the boundary ∂D, in the sense that $d {(x, D^{C})}^{2} V (x) \to \infty$ as $d (x, D^{C}) \to 0$ . We also prove bounds from above and below for Tr(exp[-tH]), and in particular we give criterions for the finiteness of...

On the equation $n (n + d) \dots (n + (i ₀ - 1) d) (n + (i ₀ + 1) d) \dots (n + (k - 1) d) = y^{l}$ with 0 < i₀ < k-1

N. Saradha, T. N. Shorey (2007)

Acta Arithmetica

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Soliton solutions for quasilinear Schrödinger equation with critical exponential growth in $ℝ^{N}$

Caisheng Chen, Hongxue Song (2016)

Applications of Mathematics

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In this work, we study the existence of nonnegative and nontrivial solutions for the quasilinear Schrödinger equation $- Δ_{N} u + b {| u |}^{N - 2} u - Δ_{N} (u^{2}) u = h (u), x \in ℝ^{N},$ where $Δ_{N}$ is the $N$ -Laplacian operator, $h (u)$ is continuous and behaves as $exp (α | u |^{N / (N - 1)})$ when $| u | \to \infty$ . Using the Nehari manifold method and the Schwarz symmetrization with some special techniques, the existence of a nonnegative and nontrivial solution $u (x) \in W^{1, N} (ℝ^{N})$ with $u (x) \to 0$ as $| x | \to \infty$ is established.