Search results for " Bundle"

Families of Two-dimensional Vector Fields

1998

In this section we will consider individual vector fields. They can be considered as 0-parameter families. We assume these vector fields to be of class at least C 1. This will be sufficient to ensure the existence and uniqueness of the flow φ(t, x) (t is time, x ∈ S, the phase space) and the qualitative properties which we mention below.

Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline

2019

In this chapter we will state a result asserting that for elliptic semi-classical (pseudo-)differential operators the eigenvalues are distributed according to Weyl’s law “most of the time” in a probabilistic sense. The first three sections are devoted to the formulation of the results and in the last section we give an outline of the proof that will be carried out in Chaps. 16 and 17.

Bifurcations of Regular Limit Periodic Sets

1998

In this chapter, (X λ ) will be a smooth or analytic (in Section 3) family of vector fields on a phase space S, with parameter λ ∈ P, as in Chapter 1. Periodic orbits and elliptic singular points which are limits of sequences of limit cycles are called regular limit periodic sets. The reason for this terminology is that for such a limit periodic set Γ one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near Γ will be given by a smooth equation and the theory of bifurcations of limit cycles from Γ will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the …

Invariants of equivariant algebraic vector bundles and inequalities for dominant weights

1998

Steady-state radiation heat transfer problem

1996

In Section 8.2, we shall see that the steady-state radiative heat transfer problem can be transformed to minimization of a smooth nonquadratic functional J over a convex and closed subset of a Banach space V. To this end we firstly shortly recall some basic definitions concerning differentiability of J, because these sometimes differ in the literature.

An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds

2003

For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…

*-Representations of Partial *-Algebras

2002

This chapter is devoted to *-representations of partial *-algebras. We introduce in Section 7.1 the notions of closed, fully closed, self-adjoint and integrable *-representations. In Section 7.2, the intertwining spaces of two *-representations of a partial *-algebra are defined and investigated, and using them we define the induced extensions of a *-representation. Section 7.3 deals with vector representations for a *-representation of a partial *-algebra, which are the appropriate generalization to a *-representation of the notion of generalized vectors described in Chapter 5. Regular and singular vector representations are defined and characterized by the properties of the commutant, and…

Andreklassingers arbeid med problemløsningsoppgaver : Et semiotisk perspektiv

2019

Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2019 This master thesis presentsaqualitative case study whichexplore year 2 students work with problem solving tasks, in a semiotic perspective. In the study, three small groups were observed while working with problem solving tasks. The aim of the observations where to getaninsight into which semiotic resources the students used while working onthe problem solving tasks. Video recordings from the observations make up the empirical data material of this study. This study is placed in the socio-cultural learning perspective. The aim of this study is to explore which semiotic resources the students use while working onproblem sol…

The impact of service bundles on the mechanism through which functional value and price value affect WOM intent

2017

Purpose The purpose of this paper is to contribute toward the current limited understanding of service bundles by investigating how purchasers of combined product-service bundles (bundle customers) differ from those purchasing a product and associated service separately (non-bundle customers). Design/methodology/approach The hypothesized effects were tested on a representative sample of mobile phone subscribers in Finland, through a multi-group moderated analysis using variance-based structural equation modeling. Findings While functional value had a stronger effect on attitude for bundle customers, price value is a stronger determinant of attitude for non-bundle customers. There was no di…

Cortical Bundles in the Persistent, Photosynthetic Stems of Cacti

1992

We examined 62 species in 45 genera of the cactus subfamily Cactoideae; all had collateral cortical bundles that permeated the broad, water-storing inner cortex and extended to the base of the outer, photosynthetic palisade cortex. Mean distance between cortical bundles was 0.75 mm, similar to the mean spacing (0.74 mm) of veins in leaves of Pereskia, a genus of relict leaf-bearing cacti. In 16 species, both young and extremely old stem cortex was available for study: in all of these, older bundles had larger amounts of phloem than did younger bundles, indicating that phloem had been produced for many years. In ten species, older bundles also had more xylem than younger bundles. In two gene…