Search results for "Maxima"
showing 10 items of 371 documents
Signal Restoration via a Splitting Approach
2012
International audience; In the present study, a novel signal restoration method from noisy data samples is presented and is termed as "signal split (SSplit)" approach. The new method utilizes Stein unbiased risk estimate estimator to split the signal, the Lipschitz exponents to identify noise elements and a heuristic approach for the signal reconstruction. However, unlike many noise removal techniques, the present method works only in the non-orthogonal domain. Signal restoration was performed on each individual part by finding the best compromise between the data samples and the smoothing criteria. Statistical results are quite promising and suggest better performance than the conventional…
A new definition of well-behaved discrimination functions
2009
Abstract A discrimination function shows the probability or degree with which stimuli are discriminated from each other when presented in pairs. In a previous publication [Kujala, J.V., & Dzhafarov, E.N. (2008). On minima of discrimination functions. Journal of Mathematical Psychology , 52 , 116–127] we introduced a condition under which the conformity of a discrimination function with the law of Regular Minimality (which says, essentially, that “being least discriminable from” is a symmetric relation) implies the constancy of the function’s minima (i.e., the same level of discriminability of every stimulus from the stimulus least discriminable from it). This condition, referred to as “well…
Integral binary Hamiltonian forms and their waterworlds
2018
We give a graphical theory of integral indefinite binary Hamiltonian forms $f$ analogous to the one by Conway for binary quadratic forms and the one of Bestvina-Savin for binary Hermitian forms. Given a maximal order $\mathcal O$ in a definite quaternion algebra over $\mathbb Q$, we define the waterworld of $f$, analogous to Conway's river and Bestvina-Savin's ocean, and use it to give a combinatorial description of the values of $f$ on $\mathcal O\times\mathcal O$. We use an appropriate normalisation of Busemann distances to the cusps (with an algebraic description given in an independent appendix), and the $\operatorname{SL}_2(\mathcal O)$-equivariant Ford-Voronoi cellulation of the real …
Failure of topological rigidity results for the measure contraction property
2014
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.
The variation of the maximal function of a radial function
2017
We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.
Ein Kriterium f�r die Approximierbarkeit von Funktionen aus sobolewschen R�umen durch glatte Funktionen
1981
The present paper provides a necessary and sufficient criterion for an element of a Sobolev space W k p (Ω) to be approximated in the Sobolev norm by Ck(En)-smooth functions. Here Ω is a bounded open set of n-dimensional Euclidean space En with convex closure $$\bar \Omega$$ and boundary ∂Ω having n-dimensional Lebesgue measure zero. No further boundary regularity (such as e.g. the segment property) is required.Our main tools are the Hardy-Littlewood maximal functions and a slightly strengthened version of a well-known extension theorem of Whitney.This work was inspired by and is very close in spirit to the pertinent parts of Calderon-Zygmund [6].
Nonlinear Robin problems with unilateral constraints and dependence on the gradient
2018
We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution.
Wavelength discrimination in the goldfish
1986
Wavelength discrimination was measured in three goldfish using a behavioral training technique. TheΔλ function has three minima which indicate spectral ranges of high discrimination ability: at 410–420 nm, at 500 nm and at 600–610 nm (Fig. 5). The best discrimination of all was found at 500 nm:Δλ as low as 4 nm. Model computations were performed to find out whether theΔλ function can be explained on the basis of the cone sensitivity functions. The results (Figs. 6 and 7) indicate that the high discrimination ability at 600–610 nm can be explained under the assumption that the long-wave cone mechanism is modified by neural interactions. The high discrimination at 410–420 nm. indicates the ex…
On the nature of slow β-relaxation in supercooled liquids
2000
We propose a model for reorientational motions of molecules associated with secondary beta-relaxation in supercooled liquids. The secondary relaxation is attributed to relaxation within a given local minimum, while the primary relaxation is attributed to transitions between distinct free-energy minima. We find that (i) at the temperature where the peak frequency of the extrapolated beta-relaxation intersects the alpha-relaxation, the actual and the extrapolated spectra differ in their time constants by approximately one decade; (ii) there is no clear division between the imaginary part of the dielectric susceptibility for the alpha- and the beta-relaxation for temperatures larger than 1.1 T…
Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
2011
AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.