Search results for "Calculus"
showing 10 items of 617 documents
A boundary min-max principle as a tool for boundary element formulations
1991
Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.
Non-linear oscillators under parametric and external poisson pulses
1994
The extended Ito calculus for non-normal excitations is applied in order to study the response behaviour of some non-linear oscillators subjected to Poisson pulses. The results obtained show that the non-normality of the input can strongly affect the response, so that, in general, it can not be neglected.
Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus
2023
Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.
Assessing use and suitability of scanning electron microscopy in the analysis of micro remains in dental calculus
2014
AbstractDental calculus is increasingly recognized as a major reservoir of dietary information. Palaeodietary studies using plant and animal micro remains (e.g. phytoliths, pollen, sponge spicules, and starch grains) trapped in calculus have the potential to revise our knowledge of the dietary role of plants in past populations. The conventional methods used to isolate and identify these micro remains rely on removing them from their microenvironment in the calculus, thus the microenvironment that traps and preserves micro remains is not understood. By using scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM–EDX) on modern chimpanzee calculus from the Taï Forest, Côt…
The Principle of the Transcendental Deduction. The First Section of the Deduction of the Pure Concepts of the Understanding
2019

 This paper considers the transcendental deduction of the categories from a specific point of view: the First Section of the Deduction of the Pure Concepts of the Understanding. In this passage, Kant not only explores the task and the method of the transcendental deduction, in form of the principle of the transcendental deduction, but also implements it. The subsequent section(s) of the deduction proceed(s) to build on the argument, and do(es) so in different ways in the A- and the B-deduction. Accordingly, the principle of the transcendental deduction has a crucial function for the entire deduction because it builds a transition between the first and the following section(s) in whic…
Dental calculus is not equivalent to bone collagen for isotope analysis: a comparison between carbon and nitrogen stable isotope analysis of bulk den…
2014
Palaeodietary reconstruction using the carbon and nitrogen isotope values of bone and dentine collagen is a well-established method and the biochemical processes involved are well known. Researchers have recently explored using bulk samples of dental calculus as a substitute for bone and dentine collagen in dietary analyses, because calculus can be sampled without causing damage to the teeth, and may be useful in situations where more destructive analyses are not possible, or where collagen is poorly preserved. Several questions remain about the use of bulk calculus as a source of carbon and nitrogen isotope data, however. It is not yet clear how much of an individual¿s life span dental cal…
Fuzzy tuning systems: the mathematics of musicians
2005
We present some mathematical properties which determine tuning methods. We introduce the concept of fuzzy tuning systems and we analyze four of the systems coexisting within the current orchestras: Pythagorean, Just Intonation, Holder's and Equal Temperament systems. We show that the theoretical and practical tuning methods are the same. We introduce the idea of compatibility between tuning systems and we give some sufficient conditions to determine an appropriate number of notes into which the octave must be divided.
Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD
2016
The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative …
Two properties of Müntz spaces
2017
Abstract We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.
Stochastic differential calculus for wind-exposed structures with autoregressive continuous (ARC) filters
2008
In this paper, an alternative method to represent Gaussian stationary processes describing wind velocity fluctuations is introduced. The technique may be considered the extension to a time continuous description of the well-known discrete-time autoregressive model to generate Gaussian processes. Digital simulation of Gaussian random processes with assigned auto-correlation function is provided by means of a stochastic differential equation with time delayed terms forced by Gaussian white noise. Solution of the differential equation is a specific sample of the target Gaussian wind process, and in this paper it describes a digitally obtained record of the wind turbolence. The representation o…