Search results for "Functional analysis"
showing 9 items of 1059 documents
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed
A case formulation model for the assessment of psychological problems among deafblind persons
2012
In order to describe and understand possible problems associated with deafblindness we applied a functional analysis case formulation strategy and Functional Analytic Clinical Case Diagrams (FACCD). We collected clinical assessment data from deafblind persons who were experiencing multiple psychological problems as reported by their healthcare professionals. The data were collected after the healthcare professionals were trained in functional analyses and in applying FACCD. The 21 deafblind persons assessed by healthcare professionals were reported to have 3–11 psychological problems. Two case examples are given to illustrate the complexity of a deafblind person's life situation and the fun…
Spontaneous Raman Scattering Spectrum of Gaseous IrF6 in the Ground Electronic State
1996
On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension
2005
We investigate the low-lying spectrum of Witten–Laplacians on forms of arbitrary degree in the semi-classical limit and uniformly in the space dimension. We show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum. Moreover, we are able to count the number of eigenvalues in each cluster. We apply our results to certain sequences of Schrodinger operators having strictly convex potentials and show that some well-known results of semi-classical analysis hold also uniformly in the dimension.
Robust H<inf>&#x221E;</inf> control of Markovian jump systems with mixed time delays
2010
In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…
Applying functional analysis for studying intimately violent men
2008
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…
Fractional Hardy inequalities and visibility of the boundary
2013
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.
Compression and load balancing for efficient sparse matrix-vector product on multicore processors and graphics processing units
2021
We contribute to the optimization of the sparse matrix-vector product by introducing a variant of the coordinate sparse matrix format that balances the workload distribution and compresses both the indexing arrays and the numerical information. Our approach is multi-platform, in the sense that the realizations for (general-purpose) multicore processors as well as graphics accelerators (GPUs) are built upon common principles, but differ in the implementation details, which are adapted to avoid thread divergence in the GPU case or maximize compression element-wise (i.e., for each matrix entry) for multicore architectures. Our evaluation on the two last generations of NVIDIA GPUs as well as In…