Using the spectral subspaces obtained in [HS], Brown’s results (cf. [Bro]) on the Brown measure of an operator in a type II1 factor (M, τ) are generalized to finite sets of commuting operators in M. It is shown that whenever T1, . . . , Tn ∈ M are mutually commuting operators, there exists one and only one compactly supported Borel probability measure μT1,...,Tn on B(C) such that for all α1, . ...

We used participant-produced photography to investigate everyday commuting practices in Cambridge, UK. Photovoice served as an observational method for producing ethnographically rich data. A total of 19 participants produced over 500 photos about their journeys to and from work and took part in photo-elicitation interviews. Three themes emerged. First, many images depicted 'well-being' in comm...

At city level, personal monitoring is the best way to assess people's exposure. However, it is usually estimated from a few monitoring stations. Our aim was to determine the exposure to black carbon (BC) and BC dose for 45 schoolchildren with portable microaethalometers and to evaluate the relationship between personal monitoring and fixed stations at schools (indoor and outdoor) and in an urba...

This paper is twofold. First we prove a common fixed point theorem for a pair of weakly compatible mappings along with E.A. property. This theorem improves and generalizes a result of Jungck [5] without any continuity requirement besides relaxing the containment of the range of one map into the range of other map. Moreover, we prove some results under different variants of R-weakly commuting ma...

Let d > 1, and let (X,α) and (Y, β) be two zeroentropy Z-actions on compact abelian groups by d commuting automorphisms. We show that if all lower rank subactions of α and β have completely positive entropy, then any measurable equivariant map from X to Y is an affine map. In particular, two such actions are measurably conjugate if and only if they are algebraically conjugate.

Let R be a ring with center Z(R). We write the commutator [x, y] = xy− yx, (x, y ∈ R). The following commutator identities hold: [xy,z] = x[y,z] + [x,z]y; [x, yz] = y[x,z] + [x, y]z for all x, y,z ∈ R. We recall that R is prime if aRb = (0) implies that a= 0 or b = 0; it is semiprime if aRa = (0) implies that a = 0. A prime ring is clearly a semiprime ring. A mapping f : R→ R is called centrali...

Given commuting families of Hermitian matrices {A1, . . . , Ak} and {B1, . . . , Bk}, conditions for the existence of a completely positive map Φ, such that Φ(Aj) = Bj for j = 1, . . . , k, are studied. Additional properties such as unital or / and trace preserving on the map Φ are also considered. Connections of the study to dilation theory, matrix inequalities, unitary orbits, and quantum inf...

Location Based Services (LBS) provide a new perspective for spatiotemporally analyzing dynamic urban systems. Research has investigated urban dynamics using GSM (Global System for Mobile Communications), GPS (Global Positioning System), SNS (Social Networking Services) and Wi-Fi techniques. However, less attention has been paid to the analysis of urban structure (especially commuting pattern) u...

Here the solid arrows represent maps that are given, and the problem is to find a map h commuting in the diagram. Usually the map i is an inclusion, and p is some kind of “bundle map” such as a local product. Note the special cases: (i) if i is an inclusion, E = A, and f = 1A, then the extension problem asks whether A is a retract of X; and (ii) if p is surjective, X=B, and g = 1B, the lifting ...