Search results for "Logarithm"
showing 10 items of 182 documents
Effects of divergent ghost loops on the Green’s functions of QCD
2013
In the present work we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, whose origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, whose perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d=4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d=3 they are linear, giving rise to enhanced effects. In the ca…
Machine learning for energy cost modelling in wastewater treatment plants.
2018
Understanding the energy cost structure of wastewater treatment plants is a relevant topic for plant managers due to the high energy costs and significant saving potentials. Currently, energy cost models are generally generated using logarithmic, exponential or linear functions that could produce not accurate results when the relationship between variables is highly complex and non-linear. In order to overcome this issue, this paper proposes a new methodology based on machine-learning algorithms that perform better with complex datasets. In this paper, machine learning was used to generate high-performing energy cost models for wastewater treatment plants, using a database of 317 wastewater…
On some inequalities for the identric, logarithmic and related means
2015
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex
2018
The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as &ldquo
Radial growth of solutions to the poisson equation
2001
We establish a radial growth estimate of the type of the iterated law of the logarithm for solutions to the Poisson equation in the unit ball.
From $1$ to $6$: a finer analysis of perturbed branching Brownian motion
2020
The logarithmic correction for the order of the maximum for two-speed branching Brownian motion changes discontinuously when approaching slopes $\sigma_1^2=\sigma_2^2=1$ which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing $\sigma_1^2=1\pm t^{-\alpha}$ and $\sigma_2^2=1\pm t^{-\alpha}$. We show that the logarithmic correction for the order of the maximum now smoothly interpolates between the correction in the iid case $\frac{1}{2\sqrt 2}\ln(t),\;\frac{3}{2\sqrt 2}\ln(t)$ and $\frac{6}{2\sqrt 2}\ln(t)$ when $0<\alpha<\frac{1}{2}$. This is due to the localisation of extremal particles at the time of speed change which depen…
Simulating Term Structure of Interest Rates with Arbitrary Marginals
2007
Decision models under uncertainty need to be feeded with scenarios of the interest rate curve. Such scenarios have to comply, as close as possible, with the empirical distribution of each rate. Simulation models of the term structure usually assume that the conjugate distribution of the interest rates is lognormal. Dynamic models, like vector auto-regression, implicitly postulate that the logarithm of the interest rates is normally distributed. Statistical analyses have, however, shown that stationary transformations (yield changes) of the interest rates are substantially leptokurtic, thus posing serious doubts on the reliability of the available models. We propose in this paper a vector au…
Description of the retention behaviour of solutes in micellar liquid chromatography with organic modifiers: Comparison of two methods
1995
Two methods for the description of the retention behaviour of solutes in micellar liquid chromatography are compared. One of them divides the parameter space into triangular subspaces, fitting a different equation in each subspace. The second method makes use of a unique equation, valid in the whole parameter space. In both cases, equations of the type log k=f (μ, ϕ), and 1/k=f (μ, ϕ), (μ and ϕ are the concentration of surfactant and alcohol, respectively), were used to describe the retention. The use of the hyperbolic function, 1/k=c0+c1μ+c3μϕ, to describe the whole parameter space yielded the best prediction. When a small portion of the parameter space was modelled, a simpler hyperbolic f…
Stationary–mobile phase distribution coefficient for polystyrene standards
2002
The measured shifts of the retention volume V R of polystyrene (PS) towards lower values in benzene–methanol (Bz–MeOH), and towards higher values in butanone–heptane (But–Hep) are in agreement with our theoretical model, in which both MeOH and But are adsorbed on Lichrospher. This paved way for us to model the chromatographic stationary (s)-phase as MeOH and the mobile (m)-phase as Bz–MeOH, and to calculate the distribution coefficients for PS. For But–Hep, the s-phase has been modeled as But, and the m-phase as But–Hep. A linear relation for the experimental equilibrium distribution P sm of PS is shown between the s- and m- phases in Bz–MeOH and But–Hep vs. the logarithm of the molecular m…
The Bruce–Roberts Number of A Function on A Hypersurface with Isolated Singularity
2020
AbstractLet $(X,0)$ be an isolated hypersurface singularity defined by $\phi \colon ({\mathbb{C}}^n,0)\to ({\mathbb{C}},0)$ and $f\colon ({\mathbb{C}}^n,0)\to{\mathbb{C}}$ such that the Bruce–Roberts number $\mu _{BR}(f,X)$ is finite. We first prove that $\mu _{BR}(f,X)=\mu (f)+\mu (\phi ,f)+\mu (X,0)-\tau (X,0)$, where $\mu $ and $\tau $ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen–Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which the hypersurface $(X,0)$ was assumed to be weighted homogeneous.