Search results for "Valence"
showing 10 items of 2732 documents
Nonexistence of Quasiconformal Maps Between Certain Metric Measure Spaces
2013
We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application, we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.
Long-Term Development of How Students Interpret a Model: Complementarity of Contexts and Mathematics
2017
When students engage in rich mathematical modelling tasks, they have to handle real-world contexts and mathematics in chorus. This is not easy. In this chapter, contexts and mathematics are perceived as complementary, which means they can be integrated. Based on four types of approaches to modelling tasks (ambivalent, reality bound, mathematics bound or integrating), we used task-based interviews to study the development of students’ approaches while the students moved from grade 11 to 12. Our participants were ten Dutch students. We found that their approaches initially were either ambivalent, reality bound or mathematics bound. In subsequent interviews, the preference was maintained, and …
Equivalence Relations on Stonian Spaces
1996
Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.
Multi-resolution analysis generated by a seed function
2009
In this paper we use the equivalence result originally proved by the author, which relates a multiresolution analysis (MRA) of ℒ2(R) and an orthonormal set of single electron wave functions in the lowest Landau level, to build up a procedure which produces, starting with a certain square-integrable function, a MRA of ℒ2(R). © 2003 American Institute of Physics.
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…
AC is Equivalent to the Coherence Principle. Corrigendum to my Paper "Induction Principles for Sets"
2009
Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property for partial functions contained in a relation are formulated. The equivalence of the coherent principles with AC and the equivalence of the ultrafilter property with BPI is shown.
Exchange transfer in high-nuclearity mixed valence magnetic clusters: Theoretical approach and expected manifestations
1998
Abstract We report here a general solution of the exchange transfer problem in the high-nuclearity mixed valence clusters containing arbitrary number of itinerant electrons. The concept of two kinds of exchange transfer, namely kinetic and potential, is introduced by analogy with basic Anderson's mechanisms of the magnetic exchange. The kinetic exchange transfer is treated as a second order transfer process between two centres through the excited state of a third centre. The potential exchange transfer is also considered as a three-centre interaction but in this case only the ground states of the constituent ions are involved. The actual parameters of the exchange transfer are expected to b…
Conformational behaviour of 2,2?-bipyrrole
1986
The rotational potential around the interannular bond in 2,2′-bipyrrole has been calculated making use of standard minimal STO-3G and split valence 4-31G basis sets. Geometrical optimization concerning the most significant interannular internal parameters has been performed with both basis sets. The trans conformer is predicted to be more stable than the cis. The minimal basis set predicts the existence of a cisoid-gauche minimum which after limited optimization becomes very shallow and it seems to be an artifact of the rigid rotor approximation. At 4-31G level, both the trans and cis conformers represent maxima in the potential curve and two gauche minima appear at θ=46.0° and θ=147.6°, th…
The burden of mental disorders, substance use disorders and self-harm among young people in Europe, 1990–2019: Findings from the Global Burden of Dis…
2022
Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAM
Blisters and calluses from rowing : prevalence, perceptions and pain tolerance
2022
Background and Objectives: Rowing is a sport that involves constant gripping, pulling/pushing, and rotational movements of the hands, in a cyclic periodic manner with every stroke, with hundreds of strokes being taken within a short period of time. Dermatological issues on rowers’ hands (fingers and palms) in the form of blisters and calluses are common knowledge within the community, but their prevalence and the rower’s perceptions and pain tolerance to them has never been systematically evaluated. This work addresses these lacunae. Materials and Methods: Analysis of data collected from a survey on a sample of competitive (117) and noncompetitive rowers (28) who row on-water (total 145). R…