Search results for "approximation"
showing 10 items of 818 documents
Unique continuation property and Poincar�� inequality for higher order fractional Laplacians with applications in inverse problems
2020
We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq 0$. We apply the results to show that one can uniquely recover, up to a gauge, electric and magnetic potentials from the Dirichlet-to-Neumann map associated to the higher order fractional magnetic Schr\"odinger equation. We also study the higher order fractional Schr\"odinger equation with singular electric potential. In both cases, we obtain a Runge approximation property for the equation. Furthermore, we prove a uniqueness result for a partial data problem of the $d$-…
The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties
2020
These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory.
Stability of the fixed point property in Hilbert spaces
2005
In this paper we prove that if X X is a Banach space whose Banach-Mazur distance to a Hilbert space is less than 5 + 17 2 \sqrt {\frac {5+\sqrt {17}}{2}} , then X X has the fixed point property for nonexpansive mappings.
Tensor products of Fréchet or (DF)-spaces with a Banach space
1992
Abstract The aim of the present article is to study the projective tensor product of a Frechet space and a Banach space and the injective tensor product of a (DF)-space and a Banach space. The main purpose is to analyze the connection of the good behaviour of the bounded subsets of the projective tensor product and of the locally convex structure of the injective tensor product with the local structure of the Banach space.
WEAKLY COMPACT HOMOMORPHISMS BETWEEN SMALL ALGEBRAS OF ANALYTIC FUNCTIONS
2001
The weak compactness of the composition operator CΦ(f) = f ○ Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.
On the nonarchimedean quadratic Lagrange spectra
2018
We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic irrationals under the modular group. We give nonarchimedean analogs of various well known results in the real case: the closedness and boundedness of the Lagrange spectrum, the existence of a Hall ray, as well as computations of various Hurwitz constants. We use geometric methods of group actions on Bruhat-Tits trees. peerReviewed
Chromatographic multivariate quality control of pharmaceuticals giving strongly overlapped peaks based on the chromatogram profile
2004
In the present paper, the simultaneous quantification of two analytes showing strongly overlapped chromatographic peaks (alpha = 1.02), under the assumption that both available equipment and training of the laboratory staff are basic, is studied. A pharmaceutical preparation (Mutabase) containing two drugs of similar physicochemical properties (amitriptyline and perphenazine) is selected as case of study. The assays are carried out under realistic working conditions (i.e. routine testing laboratories). Uncertainty considerations are introduced in the study. A partial least squares model is directly applied to the chromatographic data (with no previous signal transformation) to perform quali…
Electronic structure, lattice dynamics and thermodynamic stability of paramelaconite Cu4O3
2014
Abstract An ab initio study of the electronic structure, lattice dynamic and thermodynamic properties of paramelaconite Cu 4 O 3 is reported. The insulating, mixed-valence character of Cu 4 O 3 is elucidated by analyzing the band structure and the spin-orbital symmetry of the Cu-3 d hole states. Exchange coupling constants between Cu 2+ ions are computed which confirm the frustrated antiferromagnetism of the spin lattice. The lattice dynamics is studied from first principles and main features of the vibrational spectrum are assigned to the different chemical species Cu + , Cu 2+ and O. The thermodynamic stability of Cu 4 O 3 is investigated by calculating the free energy of the decompositio…
Power-law hereditariness of hierarchical fractal bones
2013
SUMMARY In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann–Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related …
Extended GT-STAF information indices based on Markov approximation models
2013
Abstract A series of novel information theory-based molecular parameters derived from the insight of a molecular structure as a chemical communication system were recently presented and usefully employed in QSAR/QSPRs (J. Comp. Chem, 2013, 34, 259; SAR and QSAR in Environ. Res. 2013, 24). This approach permitted the application of Shannon’s source and channel coding entropic measures to a chemical information source comprised of molecular ‘fragments’, using the zero-order Markov approximation model (atom-based approach). This report covers the theoretical aspects of the extensions of this approach to higher-order models, introducing the first, second and generalized-order Markov approximati…