Search results for "Calculus"

Dental disease and dietary isotopes of individuals from St Gertrude Church cemetery, Riga, Latvia.

2018

This research explores oral health indicators and stable carbon and nitrogen isotope data to explore diet, and differences in diet, between people buried in the four different contexts of the St Gertrude Church cemetery (15th– 17th centuries AD): the general cemetery, two mass graves, and a collective mass burial pit within the general cemetery. The main aim is to assess whether people buried in the mass graves were rural immigrants, or if they were more likely to be the victims of plague (or another epidemic) who lived in Riga and its suburbs. The data produced (from dental disease assessments and isotope analyses) were compared within, as well as between, the contexts. Most differences em…

On Modern Matrix Iteration Processes of Bernoulli and Graeffe Type

1958

Historical Part—Calculus of Variations

2018

The calculus of variations is an old mathematical discipline and historically finds its origins in the introduction of the brachistochrone problem at the end of the 17th century by Johann Bernoulli to challenge his contemporaries to solve it. Here, we briefly introduce the reader to the main results.

Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery

2019

Abstract We discuss the hereditary behavior of hydroxyapatite-based composites used for cranioplasty surgery in the context of material isotropy. We classify mixtures of collagen and hydroxiapatite composites as biomimetic ceramic composites with hereditary properties modeled by fractional-order calculus. We assume isotropy of the biomimetic ceramic is assumed and provide thermodynamic of restrictions for the material parameters. We exploit the proposed formulation of the fractional-order isotropic hereditariness further by means of a novel mechanical hierarchy corresponding exactly to the three-dimensional fractional-order constitutive model introduced.

Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics

2010

This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…

A generalized model of elastic foundation based on long-range interactions: Integral and fractional model

2009

The common models of elastic foundations are provided by supposing that they are composed by elastic columns with some interactions between them, such as contact forces that yield a differential equation involving gradients of the displacement field. In this paper, a new model of elastic foundation is proposed introducing into the constitutive equation of the foundation body forces depending on the relative vertical displacements and on a distance-decaying function ruling the amount of interactions. Different choices of the distance-decaying function correspond to different kind of interactions and foundation behavior. The use of an exponential distance-decaying function yields an integro-d…

Mechanically-based approach to non-local elasticity: Variational principles

2010

Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…

Microremains from El Mirón Cave human dental calculus suggest a mixed plant/animal subsistence economy during the Magdalenian in Northern Iberia

2015

Abstract Despite more than a century of detailed investigation of the Magdalenian period in Northern Iberia, our understanding of the diets during this period is limited. Methodologies for the reconstruction of Late Glacial subsistence strategies have overwhelmingly targeted animal exploitation, thus revealing only a portion of the dietary spectrum. Retrieving food debris from calculus offers a means to provide missing information on other components of diet. We undertook analysis of human dental calculus samples from Magdalenian individuals (including the “Red Lady”) at El Miron Cave (Cantabria, Spain), as well as several control samples, to better understand the less visible dietary compo…

Threefold Introduction to Fractional Derivatives

2008

Student use of resources in Calculus and Linear Algebra

2018

International audience; In this study we have investigated the resources used by first year engineering students in a technical university in the Netherlands, for their learning of Calculus and Linear Algebra. Using a case study approach we have focused on how the resources and their use (a) differed from upper secondary school as compared to university, and (b) differed between the two university courses. The results indicate that, in terms of (a) students built on secondary school experiences and emulated these into their university courses, where some subsequently experienced difficulties. In terms of (b), we argue that the course organization and the alignment of curriculum materials wi…