Academic literature on the topic 'L-Gauss transform'

The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires [Formula: see text] operations, where M𝓁 is the number of Fourier components along dimension 𝓁, N is the number of irregularly spaced samples, and ε is the required accuracy. This is a dramatic improvement over the [Formula: see text] operations required for the direct evaluation (NDFT). The performance of the NFFT depends on the lowpass filter used in the algorithm. A truncated Gauss pulse, proposed in the literature, is optimized. A newly proposed filter, a Gauss pulse tapered with a Hanning window, performs better than the truncated Gauss pulse and the B-spline, also proposed in the literature. For small filter length, a numerically optimized filter shows the best results. Numerical experiments for 1-D and 2-D implementations confirm the theoretically predicted accuracy and efficiency properties of the algorithm.

In this paper, we revisit some fundamental properties of linear canonical transform (abbreviated as LCT). In particular, we prove the additive property rigorously for LCT in the higher dimensional case (abbreviated as MLCT). We also consider the ‐theory of MLCT with . Specifically, the inversion theorem of MLCT by the related Gauss and Abel means is studied, and the pointwise convergence of approximate identities with respect to convolution for MLCT is also obtained. As applications, we study the ‐type Heisenberg‐Pauli‐Weyl uncertainty principles and the ‐type Donoho‐Stark uncertainty principles for MLCT.

Abstract We study the one-level density for families of $L$-functions associated with cubic Dirichlet characters defined over the Eisenstein field. We show that the family of $L$-functions associated with the cubic residue symbols $\chi _n$ with $n$ square-free and congruent to 1 modulo 9 satisfies the Katz–Sarnak conjecture for all test functions whose Fourier transforms are supported in $(-13/11, 13/11)$, under the Generalized Riemann Hypothesis. This is the first result extending the support outside the trivial range $(-1, 1)$ for a family of cubic $L$-functions. This implies that a positive density of the $L$-functions associated with these characters do not vanish at the central point $s=1/2$. A key ingredient in our proof is a bound on an average of generalized cubic Gauss sums at prime arguments, whose proof is based on the work of Heath-Brown and Patterson [22, 23].

The thermal behavior of air by natural convection in a confined trapezoidal cavity, one of the walls of which is subjected to a constant heat flow in hot climates, has been analyzed numerically. The heat and mass transfers are carried out by the classical equations of natural convection. These equations are discretized using the Finite Difference Method and the algebraic systems of equations thus obtained are solved with the Thomas and Gauss algorithms. We analyze the influence of the number on the current and isothermal lines as well as the effects of the aspect ratio A = l / H and the angle of inclination φ. In particular, we have shown that convective exchanges in the cavity are preponderant for high Ra numbers. Also we have watches the increase in the values ​​of the isothermal lines and the decrease in the intensity of the streamlines for the low values ​​of A and of the angle φ.

La notion de hérisson a été introduite par R.Langevin, G.Levitt et H.Rosenberg et correspond à la réalisation géométrique des différences formelles de corps convexes sur l'espace euclidien. Par la suite, Y.Martinez-Maure a largement développé la théorie des hérissons, ce qui lui a permis, entre autres, de résoudre le problème de la conjecture d'A.D.Alexandrov en produisant un contre-exemple en 2001. Aussi, on retrouve sur l'ensemble des hérissons des relations que l'on connaît sur les corps convexes, dont, en particulier, les inégalités de Minkowski et les inégalités isopérimétriques. C'est ainsi qu'apparaît la notion de hérisson marginalement piégé, qui sont des surfaces marginalement piégées sur l'espace de Lorentz-Minkowski, vérifiant des propriétés correspondant à la notion de hérisson.L'objet de cette thèse consiste à retrouver une notion de hérisson marginalement piégé sur des espaces de Lorentz dont la courbure interne est non nulle. Il a alors été nécessaire de définir la notion de hérisson sur l'espace hyperbolique et sur l'hypersphère, où, en particulier, nous en avons étudié la correspondance avec les notions de g-convexité et de h-convexité. Nous introduisons ainsi la notion de g-hérisson, dont nous étudions la cohérence ainsi que la compatibilité avec les hérissons de l'espace euclidien, et qui doit vérifier la contrainte de pouvoir définir leur transformée de L-Gauss. Cela nous permet alors de définir les g-hérissons marginalement piégés qui sont des surfaces marginalement piégées sur les espaces de Lorentz H^3 × R et S^3 × R et dont les propriétés correspondent bien avec les g-hérissons de l'espace hyperbolique et de l'hypersphère. Il nous faut néanmoins noter que les caractéristiques géométriques des hérissons marginalement piégés de l'espace de Lorentz-Minkowski ne sont pas toutes transposables aux g-hérissons marginalement piégés, ce qui contribue à limiter significativement notre démarche
The concept of hedgeho was introduced by R.Langevin, G.Levitt, and H.Rosenberg, representing the geometric realization of formal differences of convex bodies in Euclidean space. Subsequently, Y.Martinez-Maure extensively developed the hedgehog theory, allowing him, among other things, to address the problem of A.D.Alexandrov's conjecture by providing a counterexample in 2001. Additionally, relations known for convex bodies, particularly the Minkowski inequalities and isoperimetric inequalities, are observed within the set of hedgehogs. This leads to the emergence of the notion of marginally trapped hedgehog, which refers to surfaces that are marginally trapped in the Lorentz-Minkowski space, possessing properties corresponding to the concept of hedgehog.The objective of this thesis is to explore the notion of marginally trapped hedgehogs within Lorentz spaces where the intrinsic curvature is non-zero. It was therefore essential to define the concept of hedgehogs in hyperbolic space and on the hypersphere, where we have particularly studied their correspondence with the notions of g-convexity and h-convexity. In this context, we introduce the idea of g-hedgehog, examining its coherence and compatibility with the hedgehogs in Euclidean space, and which must meet the constraint of defining their L-Gauss transformation. This enables us to define marginally trapped g-hedgehogs, which are surfaces marginally trapped in Lorentz spaces H^3 × R and S^3 × R, with properties aligning well with g-hedgehogs in hyperbolic space and on the hypersphere. However, it's crucial to note that not all geometric characteristics of marginally trapped hedgehogs in the Lorentz-Minkowski space are transferable to marginally trapped g-hedgehogs, significantly constraining our approach