Search results for "Mathematica"
showing 10 items of 7971 documents
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
On Γ-convergence of pairs of dual functionals
2011
Abstract The paper considers a slightly modified notion of the Γ-convergence of convex functionals in uniformly convex Banach spaces and establishes that under standard coercitivity and growth conditions the Γ-convergence of a sequence of functionals { F j } to F ˜ implies that the corresponding sequence of dual functionals { F j ⁎ } converges in an analogous sense to the dual to F ˜ functional F ˜ ⁎ .
The space H(Ω,(zj)) of holomorphic functions
2008
Abstract Let Ω be a domain in C n . Let H ( Ω ) be the linear space over C of the holomorphic functions in Ω, endowed with the compact-open topology. Let ( z j ) be a sequence in Ω without adherent points in Ω. In this paper, we define the space H ( Ω , ( z j ) ) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Ω and some sequences ( z j ) , the non-zero elements of H ( Ω , ( z j ) ) cannot be extended holomorphically outside Ω. As a consequence, we obtain some characterizations of the domains of holomorphy in C n .
A generalized porous medium equation related to some singular quasilinear problems
2014
Abstract In this paper we study the existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is { − ∑ m = 1 ∞ a m Δ u m = f in Ω u = 0 on ∂ Ω , where Ω is a bounded domain of R N , a m is a sequence of nonnegative real numbers, and f is in L q ( Ω ) , q > N 2 .
On the order of indeterminate moment problems
2013
For an indeterminate moment problem we denote the orthonormal polynomials by P_n. We study the relation between the growth of the function P(z)=(\sum_{n=0}^\infty|P_n(z)|^2)^{1/2} and summability properties of the sequence (P_n(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zP_n(z)=b_nP_{n+1}(z)+a_nP_n(z)+b_{n-1}P_{n-1}(z), we show that the function P is of order \alpha with 0<\alpha<1, if and only if the sequence (P_n(z)) is absolutely summable to any power greater than 2\alpha. Furthermore, the order \alpha is equal to the exponent of convergence of the sequence (b_n). Similar results are obtained for logarithmic order and for more ge…
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
2019
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…
Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategie…
2008
We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application d…
A new approach to fuzzy sets: Application to the design of nonlinear time series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillat…
2019
Abstract It is shown that characteristic functions of sets can be made fuzzy by means of the B κ -function, recently introduced by the author, where the fuzziness parameter κ ∈ R controls how much a fuzzy set deviates from the crisp set obtained in the limit κ → 0. As applications, we present first a general expression for a switching function that may be of interest in electrical engineering and in the design of nonlinear time series. We then introduce another general expression that allows wallpaper and frieze patterns for every possible planar symmetry group (besides patterns typical of quasicrystals) to be designed. We show how the fuzziness parameter κ plays an analogous role to temper…
Nonlinear pseudo-bosons
2011
In a series of recent papers the author has introduced the notion of (regular) pseudo-bosons showing, in particular, that two number-like operators, whose spectra are ${\Bbb N}_0:={\Bbb N}\cup\{0\}$, can be naturally introduced. Here we extend this construction to operators with rather more general spectra. Of course, this generalization can be applied to many more physical systems. We discuss several examples of our framework.
On the existence of the exponential solution of linear differential systems
1999
The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.