Search results for "Equation solving"
showing 7 items of 7 documents
An output-only stochastic parametric approach for the identification of linear and nonlinear structures under random base excitations: Advances and c…
2014
In this paper a time domain output-only Dynamic Identification approach for Civil Structures (DICS) first formulated some years ago is reviewed and presented in a more generalized form. The approach in question, suitable for multi- and single-degrees-of-freedom systems, is based on the statistical moments and on the correlation functions of the response to base random excitations. The solving equations are obtained by applying the Itô differential stochastic calculus to some functions of the response. In the previous version ([21] Cavaleri, 2006; [22] Benfratello et al., 2009), the DICS method was based on the use of two classes of models (Restricted Potential Models and Linear Mass Proport…
An algorithm for the solution of tree equations
1997
We consider the problem of solving equations over k-ary trees. Here an equation is a pair of labeled α-ary trees, where α is a function associating an arity to each label. A solution to an equation is a morphism from α-ary trees to k-ary trees that maps the left and right hand side of the equation to the same k-ary tree.
Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving
2020
AbstractPhysical models for equation solving typically lack feedback regarding their appropriate use. Such feedback is possible in virtual environments and could be implemented in hybrid models. Based on an epistemological analysis, this article presents a touch gesture as a way for users to signal they want to divide both sides of an equation and a design for feedback on the use of this so-called ‘division gesture’. The design is investigated by contrasting a case study, in which students used an app with the division gesture, with a preparatory study where students had to perform corresponding actions on physical manipulatives. This investigation revealed insight into feedback functions, …
The indirect force method
1990
Abstract It is known that the matrix force method shows some advantages over the displacement method for certain classes of problems, particularly in optimization and in the stress concentration analysis. Notwithstanding this, few efforts have been made to employ this method in engineering problems. In this paper, within the elastic analysis of frames and trusses, the indirect force method, utilizing beam-node type finite elements, is proposed. This method is based on the kinematical and mechanical study of nodes and of beams, the latter connected with the nodes by their first extremes according to a preliminary arrangement. In this formulation kinematical singularities are included, in the…
More Power through Symbolic Computation: Extending Stata by using the Maxima Computer algebra system
2015
Maxima is a free and open-source computer algebra system that can perform symbolic computations such as solving equations, determining derivatives of functions, obtaining Taylor series, and manipulating algebraic expressions. In this article, I present the Maxima Bridge System, which is a collection of software programs that allows Stata to interface with Maxima so that Maxima can be used for symbolic computation to transfer data from Stata to Maxima and to retrieve results from Maxima. The cooperation between Stata and Maxima provides an environment for statistical analysis in which symbolic computation can be easily used together with all the facilities supplied by Stata. In this environ…
Revisited mixed-value method via symmetric BEM in the substructuring approach
2012
Abstract Within the Symmetric Boundary Element Method, the mixed-value analysis is re-formulated. This analysis method contemplates the subdivision of the body into substructures having interface kinematical and mechanical quantities. For each substructure an elasticity equation, connecting weighted displacements and tractions to nodal displacements and forces of the same interface boundary and to external action vector, is introduced. The assembly of the substructures is performed through both the strong and weak regularity conditions of the displacements and tractions. We obtain the solving equations where the compatibility and the equilibrium are guaranteed in the domain Ω for the use of…
Multimodal Communication and Peer Interaction during Equation-Solving Sessions with and without Tangible Technologies
2023
Despite the increasing use of technologies in the classroom, there are concerns that technology-enhanced learning environments may hinder students’ communication and interaction. In this study, we investigated how tangible technologies can enhance students’ multimodal communication and interaction during equation-solving pair work compared to working without such technologies. A tangible app for learning equation solving was developed and tested in fourth and fifth-grade classrooms with two class teachers and 24 students. Video data of the interventions were analysed using deductive and inductive content analysis. Coded data were also quantified for quantitative analysis. Additionally, teac…