Search results for "Logarithm"
showing 10 items of 182 documents
A model for planktic foraminiferal shell growth
1993
In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown …
Fault detection for nonlinear networked systems based on quantization and dropout compensation: An interval type-2 fuzzy-model method
2016
Abstract This paper investigates the problem of filter-based fault detection for a class of nonlinear networked systems subject to parameter uncertainties in the framework of the interval type-2 (IT2) T–S fuzzy model-based approach. The Bernoulli random distribution process and logarithm quantizer are used to describe the measurement loss and signals quantization, respectively. In the framework of the IT2 T–S fuzzy model, the parameter uncertainty is handled by the membership functions with lower and upper bounds. A novel IT2 fault detection filter is designed to guarantee the residual system to be stochastically stable and satisfy the predefined H ∞ performance. It should be mentioned that…
Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials
2014
It is known that the Principal Poincar\'e Pontryagin Function is generically an Abelian integral. We give a sufficient condition on monodromy to ensure that it is an Abelian integral also in non generic cases. In non generic cases it is an iterated integral. Uribe [17, 18] gives in a special case a precise description of the Principal Poincar\'e Pontryagin Function, an iterated integral of length at most 2, involving logarithmic functions with only one ramification at a point at infinity. We extend this result to some non isodromic families of real Morse polynomials.
Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements
2015
Rhinomanometry can still be considered as the standard technique for the objective assessment of the ven- tilatory function of the nose. Reliable technical requirements are given by fast digital sensors and modern information technology. However, the xyimaging of the pressure-flow relation typically shows loops as a sign of hysteresis, with the need for resolution of the breath in four phases. The three pillars of 4-phase rhinomanometry (4PR) are the replacement of estimations by measurements, the introduc- tion of parameters related to the subjective sensing of obstruction, and the graphical information regarding the disturbed function of the nasal valve. In a meta-analysis of 36,563 clini…
Enumerative Aspects of the Gross-Siebert Program
2015
For the last decade, Mark Gross and Bernd Siebert have worked with a number of collaborators to push forward a program whose aim is an understanding of mirror symmetry. In this chapter, we’ll present certain elements of the “Gross-Siebert” program. We begin by sketching its main themes and goals. Next, we review the basic definitions and results of two main tools of the program, logarithmic and tropical geometry. These tools are then used to give tropical interpretations of certain enumerative invariants. We study in detail the tropical pencil of elliptic curves in a toric del Pezzo surface. We move on to a basic illustration of mirror symmetry, Gross’s tropical construction for \(\mathbb{P…
Optimisation of gradient elution with serially-coupled columns. Part I: single linear gradients.
2014
A mixture of compounds often cannot be resolved with a single chromatographic column, but the analysis can be successful using columns of different nature, serially combined through zero-dead volume junctions. In previous work (JCA 1281 (2013) 94), we developed an isocratic approach that optimised simultaneously the mobile phase composition, stationary phase nature and column length. In this work, we take the challenge of implementing optimal linear gradients for serial columns to decrease the analysis time for compounds covering a wide polarity range. For this purpose, five ACE columns of different selectivity (three C18 columns of different characteristics, a cyano and a phenyl column) we…
Simple connections between generalized hypergeometric series and dilogarithms
1997
AbstractConnections between generalized hypergeometric series and dilogarithms are investigated. Some simple relations of an Appell's function and dilogarithms are found.
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams
2000
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
A logarithmic fourth-order parabolic equation and related logarithmic Sobolev inequalities
2006
A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions and some regularity results are shown. Furthermore, we prove that the solution converges exponentially fast to its mean value in the ``entropy norm'' and in the Fisher information, using a new optimal logarithmic Sobolev inequality for higher derivatives. In particular, the rate is independent of the solution and the constant depends only on the initial value of the entropy.