Search results for "equation"
showing 10 items of 4219 documents
Homogenization of equations describing materials interacting with clouds of particles
2012
We shall describe the derivation of homogenized equations (in an asymp- totics of mean-field type) for systems consisting of a cloud of particles dispersed in a material enclosed in a bounded domain. We shall consider in particular the homoge- nization of the Stokes problem leading to the Brinkman force and the homogenization of a model describing the heat exchange between the material and the dispersed phase leading to a (time-dependent) two-temperature equation. In both cases, the homogenized equations can be rigorously derived using similar form for the correctors.
Optimal Heating of an Indoor Swimming Pool
2020
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given…
Teachers' attitudes and self-efficacy on implementing inclusive education in Japan and Finland: A comparative study using multi-group structural equa…
2018
Abstract This study aims to explore relationships between teachers' attitudes, self-efficacy, and background variables regarding inclusive education by using a sample of 359 Japanese and 872 Finnish teachers. A multi-group structural equation modelling was conducted to find similarities and differences in how the background variables predict teachers' attitudes and self-efficacy. Experience in teaching students with disabilities had a positive effect on teachers' attitudes and self-efficacy in both countries. However, teachers' teaching career and the amount of inclusive education training affected them differently in Japan and Finland. The findings could be used to improve inclusive educat…
Optimality of Increasing Stability for an Inverse Boundary Value Problem
2021
In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger equation were established by Isakov [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and by Isakov et al. [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141]. In [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141], the authors showed that the stability of this IBVP increases …
Organocatalysts Fold to Generate an Active Site Pocket for the Mannich Reaction
2017
Catalysts containing urea, thiourea and tertiary amine groups fold into a three-dimensional organized structure in solution both in the absence as well as in the presence of substrates or substrate analogues, as indicated by solution NMR and computational studies. These foldamer catalysts promote Mannich reactions with both aliphatic and aromatic imines and malonate esters. Hammett plot and secondary kinetic isotope effects provide evidence for the C-C bond forming event as the turnoverlimiting step of the Mannich reaction. Computational studies suggest two viable pathways for the C-C bond formation step, differing in the activation modes of the malonate and imine substrates. The results sh…
Self-Efficacy Between Previous and Current Mathematics Performance of Undergraduate Students: An Instrumental Variable Approach to Exposing a Causal …
2021
PurposeSelf-efficacy has been argued theoretically and shown empirically to be an essential construct for students’ improved learning outcomes. However, there is a dearth of studies on its causal effects on performance in mathematics among university students. Meanwhile, it will be erroneous to assume that results from other fields of studies generalize to mathematics learning due to the task-specificity of the construct. As such, attempts are made in the present study to provide evidence for a causal relationship between self-efficacy and performance with a focus on engineering students following a mathematics course at a Norwegian university.MethodThe adopted research design in the presen…
Boundary value problem with integral condition for a Blasius type equation
2016
The steady motion in the boundary layer along a thin flat plate, which is immersed at zero incidence in a uniform stream with constant velocity, can be described in terms of the solution of the differential equation x'''= -xx'', which satisfies the boundary conditions x(0) = x'(0) = 0, x'(∞) = 1. The author investigates the generalized boundary value problem consisting of the nonlinear third-order differential equation x''' = -trx|x|q-1x'' subject to the integral boundary conditions x(0) = x'(0) = 0, x'(∞) = λ∫0ξx(s) ds, where 0 0 is a parameter. Results on the existence and uniqueness of solutions to boundary value problem are established. An illustrative example is provided.
On modified α-ϕ-fuzzy contractive mappings and an application to integral equations
2016
Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.
On the Fast and Rigorous Analysis of Compensated Waveguide Junctions Using Off-Centered Partial-Height Metallic Posts
2007
In this paper, we present an efficient and rigorous method, based on the 3-D boundary integral-resonant-mode expansion technique, for the analysis of multiport rectangular waveguide junctions compensated with partial-height cylindrical metallic posts. The electrical performance of a great variety of commonly used wideband microwave circuits has been improved drastically thanks to the introduction of a new design parameter, i.e., the relative position of the metallic post in the structure. To the authors' knowledge, this parameter has not been taken into account in previous studies concerning compensated junctions using partial-height metallic posts. The developed tool has been successfully …
Multi-parameter analysis of the obstacle scattering problem
2022
Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.