Search results for "Tonian"
showing 10 items of 802 documents
The infrared spectrum of CH 3 D between 900 and 3200 cm −1 : extended assignment and modeling
2000
Abstract The high resolution infrared spectrum of CH 3 D in the region from 900 to 3200 cm −1 has been analyzed on the basis of Fourier transform spectra recorded at Kitt Peak and at Giessen. A theoretical model for an effective hamiltonian in terms of irreducible tensor operators recently adapted to symmetric top molecules has been used in order to consider simultaneously all available transitions between the lowest three polyads of the molecule: the Ground State (G.S.), the Triad (three interacting fundamental bands in the 8 μm region) and the Nonad (nine interacting bands in the 4 μm region). A preliminary simultaneous fit of 3467 Triad–G.S., 5208 Nonad–G.S., and 2487 Nonad–Triad (hot ba…
Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach.
2013
A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin…
Elastohydrodynamic Collision of Two Spheres Allowing Slip on Their Surfaces.
2000
Our goal is to study theoretically the effect of deformation on the collision of two solid spheres allowing slip on their surfaces. The deformed shape of the solid surface is determined via an asymptotic technique assuming that deformation is small compared with the separation between the surfaces. It has previously been shown that the slippage makes collision possible even without any surface attractive force. Here we demonstrate that even a small amount of deformation can preclude spheres from coagulation. Copyright 2000 Academic Press.
Integrability of the one dimensional Schrödinger equation
2018
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.
A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems
2010
We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.
Validating the early childhood classroom observation measure in first and third grade classrooms
2016
The present study reports on the psychometric properties of the Early Childhood Classroom Observation Measure (ECCOM) in Finnish and Estonian first and third grade classrooms. The observation data were collected from 91 first grade teachers and 70 third grade teachers. Teachers' curriculum goals, teaching experience and the classroom size were measured also. The results of confirmatory factor analysis provided evidence of the three-factor model (management, climate, and instruction) for each dimension—child-centred, teacher-directed, and child-dominated—in both grades. The reliability of the dimensions and sub-scales was good, and some evidence was also found for criterion validity. The fin…
A Study on Engineering Freshman Conceptual Understanding of Newtonian Mechanics
2021
Force concept inventory is a multiple-choice questionnaire commonly used to assess students’ conceptual understanding of Newtonian mechanics. We here show that a cluster analysis method can be used to study student answers to the force concept inventory to investigate their understanding of Newtonian mechanics and provide new insights into the use of the force concept inventory. We identi- fied groups of students characterized by similar correct answers as well as by non- correct answers to the questionnaire, whose analysis allowed us to highlight student misconceptions/non-normative conceptions. Such an analysis of student answers gave us insights into the relationships between the student…
Classroom management practices and their associations with children’s mathematics skills in two cultural groups
2014
The aim of the study was to examine the extent to which contextual factors predict children’s mathematics skills in different cognitive domains. The sample consisted of 1734 students from 26 Estonian- and 17 Russian-language schools in Estonia. Mathematics and non-verbal reasoning tests were carried out at the beginning of the third grade. In addition, teachers were asked about their classroom management practices. The results of multilevel modelling showed that applying supportive practices in the classroom contributes to higher achievement in mathematics. Teachers from Estonian- and Russian-language schools were also found to differ with regard to their management practices, and these pra…
Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems
1999
The tangential Hilbert 16th problem is to place an upper bound for the number of isolated ovals of algebraic level curves { H ( x , y ) = const } \{H(x,y)=\operatorname {const}\} over which the integral of a polynomial 1-form P ( x , y ) d x + Q ( x , y ) d y P(x,y)\,dx+Q(x,y)\,dy (the Abelian integral) may vanish, the answer to be given in terms of the degrees n = deg H n=\deg H and d = max ( deg P , deg Q ) d=\max (\deg P,\deg Q) . We describe an algorithm producing this upper bound in the form of a primitive recursive (in fact, elementary) function of n n and d d for the particular case of hyperelliptic polynomials H ( x , y ) = y 2 + U ( x ) H(x,y)=y^2+U(x) under the additional as…
ℓ-distant Hamiltonian walks in Cartesian product graphs
2009
Abstract We introduce and study a generalisation of Hamiltonian cycles: an l-distant Hamiltonian walk in a graph G of order n is a cyclic ordering of its vertices in which consecutive vertices are at distance l. Conditions for a Cartesian product graph to possess such an l-distant Hamiltonian walk are given and more specific results are presented concerning toroidal grids.