Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A Variationally Consistent Time Modelling of Elastic-Plastic Constitutive Equations
1991
A general energy-based time discretization method for evolutive analysis is presented. Most known time integration procedures (mid-point rule, backward difference, etc.) are shown to be particular cases of it. For space continuous systems, a sequence of weighted boundary value problems of deformation-theory plasticity are obtained, each characterizable by a number of variational principles useful for finite element discretization.
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…
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…
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.
Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws
2012
Adaptive mesh refinement is nowadays a widely used tool in the numerical solution of hyperbolic partial differential equations. The algorithm is based on the numerical approximation of the solution of the equations on a hierarchical set of meshes with different resolutions. Among the different parts that compose an adaptive mesh refinement algorithm, the decision of which level of resolution is adequate for each part of the domain, i.e., the design of a refinement criterion, is crucial for the performance of the algorithm. In this work we analyze a refinement strategy based on interpolation errors, as a building block of a high order adaptive mesh refinement algorithm. We show that this tec…
Bifurcations of Reachable Sets Near an Abnormal Direction and Consequences
2007
We describe precisely, under generic conditions, the contact and the bifurcations of the reachable set at time T along an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin’s cone along γ, called the L ∞-sector and the L 2-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.