Search results for "Logarithm"
showing 10 items of 182 documents
Approaches to model the retention and peak profile in linear gradient reversed-phase liquid chromatography.
2012
Abstract The optimisation of the experimental conditions in gradient reversed-phase liquid chromatography requires reliable algorithms for the description of the retention and peak profile. As in isocratic elution, the linear relationship between the logarithm of the retention factor and the solvent contents is only acceptable in relatively small concentration ranges of modifier. However, more complex models may not allow an analytical integration of the general equation for gradient elution. Alternative approaches for modelling the retention in linear gradient elution are here proposed. Those based on the quadratic logarithmic model and a model proposed for normal liquid chromatography yie…
Determination of relaxation and retardation spectrum by inverse functional filtering
2010
Abstract The article is devoted for the determination of the relaxation and retardation spectrum (RRS) from monotonic time- and frequency-domain material functions by the inverse functional filters executing discrete convolution algorithms for geometrically spaced data. It is shown that the problem of RRS determination from a wide variety of material functions leads to the three inverse filtering tasks on a logarithmic time or frequency scale with the three specific frequency responses concerning: (i) the time-domain functions, (ii) the real parts and (iii) the imaginary parts of the frequency-domain functions, and three algorithms (having the versions with even and odd number of coefficien…
Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation
2020
The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, $$\Delta U^+$$ , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re $$_{\tau }$$ . In the present work, the effects of several geometrical parameters on the roughness function, i…
Applicability of the log MM - √D relationship to linear polyacrylamide gradient gel electrophoresis under a wide range of experimental conditions
1982
Recently we reported about a linear correlation between the logarithm of the size of native proteins (log mol mass or log Stokes' radius) and the square root of their migration distance (- √D) in linear polyacrylamide (PAA)-gradient gels (G. M. Rothe and H. Purkhanbaba, Electrophoresis 1982, 3, 33–42). The linearity between log MM and √D is not subject to time using homogeneous buffers in electrophoresis, no matter how the constants of the corresponding regression lines, slope and intercept change as a function of time. The realiability of this correlction has been re-examined with 0.7 mm thin gel plates and extending the time of electrophoresis under non-denaturating conditions from 2 to 9…
Circular law for sparse random regular digraphs
2020
Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…
Biophysical parameter retrieval with warped Gaussian processes
2015
This paper focuses on biophysical parameter retrieval based on Gaussian Processes (GPs). Very often an arbitrary transformation is applied to the observed variable (e.g. chlorophyll content) to better pose the problem. This standard practice essentially tries to linearize/uniformize the distribution by applying non-linear link functions like the logarithmic, the exponential or the logistic functions. In this paper, we propose to use a GP model that automatically learns the optimal transformation directly from the data. The so-called warped GP regression (WGPR) presented in [1] models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are…
High-energy evolution to three loops
2018
The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear re…
Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six
2017
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.
Resummation of Super-Leading Logarithms
2021
Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called non-global logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. This effect was discovered a long time ago, but not much is known about the higher-order behavior of these terms and their process dependence. We derive, for the first time, the all-order structure of these "super-leading logarithms" for generic $2\to l$ scattering processe…
Quantum geometry and microscopic black hole entropy
2006
9 pages, 6 figures.-- PACS nrs.: 04.60.Pp, 04.70.Dy.-- ISI Article Identifier: 000242448900013.-- Published online on Nov 28, 2006.