Search results for "calculus"
showing 10 items of 617 documents
Locally convex quasi $C^*$-normed algebras
2012
Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
On modal mu-calculus over finite graphs with bounded strongly connected components.
2010
For every positive integer k we consider the class SCCk of all finite graphs whose strongly connected components have size at most k. We show that for every k, the Modal mu-Calculus fixpoint hierarchy on SCCk collapses to the level Delta2, but not to Comp(Sigma1,Pi1) (compositions of formulas of level Sigma1 and Pi1). This contrasts with the class of all graphs, where Delta2=Comp(Sigma1,Pi1).
Deducing the USLE mathematical structure by dimensional analysis and self-similarity theory
2010
The Universal Soil Loss Equation (USLE) was originally deduced by a statistical analysis of a large data set of soil loss measurements. The multiplicative structure of the model has been criticised due to the considerable interdependence between the variables. Using the soil erosion representative variables and the reference condition adopted in the USLE, the aim of this paper was to apply dimensional analysis and self-similarity theory to deduce the functional relationship among the selected variables. The analysis yielded a multiplicative equation, similar to the USLE. Therefore, this study suggested that the USLE has a logical structure with respect to the variables used to simulate the …
Applying Finite State Process Algebra to Formally Specify a Computational Model of Security Requirements in the Key2phone-Mobile Access Solution
2015
Key2phone is a mobile access solution which turns mobile phone into a key for electronic locks, doors and gates. In this paper, we elicit and analyse the essential and necessary safety and security requirements that need to be considered for the Key2phone interaction system. The paper elaborates on suggestions/solutions for the realisation of safety and security concerns considering the Internet of Things (IoT) infrastructure. The authors structure these requirements and illustrate particular computational solutions by deploying the Labelled Transition System Analyser (LTSA), a modelling tool that supports a process algebra notation called Finite State Process (FSP). While determining an in…
Quasivarieties of Algebras
2001
This chapter plays a twofold role in the book. Firstly, the chapter surveys basic facts about quasivarieties of algebras. These facts are widely utilised in the subsequent chapters devoted to algebraizable logics. Secondly, the chapter shows how the methods initially elaborated for protoalgebraic sentential logics in the first part can be also applied in the area of equational logic. Most of the results presented in this chapter are proved by way of adapting the purely consequential methods of sentential logic to the needs of the (quasi) equational systems associated with quasivarieties of algebras.
The limit state of indefinite plates on elastoplastic continuum
1972
The limit analysis of indefinite plates resting on a continuous elastoplastic medium and subjected to a load distributed over a partial surface with a circular boundary yields the fundamental equation governing the problem. Minimum conditions are set and the solution that supplies the collapse load of the plate-soil system is found by variational calculus.
Some Notes About Distribution Frame Multipliers
2020
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of domain and boundedness are given. The case of Riesz distribution bases is examined in order to develop a symbolic calculus.
First-year university students making sense of symbols in integration
2020
International audience; This paper focuses on first year university engineering students and their sensemaking of integration and its symbolism. Through a semiotic approach, attention is given to two students and their attempt to verbally express their reflections on integration and the related meaning of symbols. Findings suggest that students tend to interpret the symbols mainly as operations, in terms of calculations to be carried out. They express uncertainty concerning what the symbols stand for, and the mathematical objects they represent. For example, the symbols ∫ and are respectively conceived of as “finding the integral with respect to x” and students are unclear on how Riemann su…
Bridging probability and calculus: the case of continuous distributions and integrals at the secondary-tertiary transition
2018
International audience; This paper focuses on two mathematical topics, namely continuous probability distributions (CPD) and integral calculus (IC). These two sectors that are linked by the formula P(a<=X<=b)=int_a^b f(x)dx are quite compartmented in teaching classes in France. The main objective is to study whether French students can mobilize the sector of IC to solve tasks in CPD and vice versa at the transition from high school to higher education. Applying the theoretical framework of the Anthropological Theory of the Didactic (ATD), we describe a reference epistemological model (REM) and use it to elaborate a questionnaire in order to test the capacity of students to bridge CPD and IC…
To meat or not to meat? New perspectives on Neanderthal ecology.
2014
Neanderthals have been commonly depicted as top predators who met their nutritional needs by focusing entirely on meat. This information mostly derives from faunal assemblage analyses and stable isotope studies: methods that tend to underestimate plant consumption and overestimate the intake of animal proteins. Several studies in fact demonstrate that there is a physiological limit to the amount of animal proteins that can be consumed: exceeding these values causes protein toxicity that can be particularly dangerous to pregnant women and newborns. Consequently, to avoid food poisoning from meat-based diets, Neanderthals must have incorporated alternative food sources in their daily diets, i…