Here, i(s) is the total number of (labelled) initial tokens (in all channels) for scenario s. Further, we need to analyse the production times of outputs, i.e., the relevant information produced, during an execution of a scenario sequence. Let the function m:Σ→N∪{0} map each ...
Hopkins and the author =-=[6]-=- generalized this to arbitrary sub-Hopf algebras of A, but still for M = F2. These are analogous to proving Nishida’s theorem [15] for various B’s. We view Theorem 1.1 as analogous to the nilpotence t......
Grafarend, E.W., Heidenreich, A.: The generalized Mollweide projection of the biaxial ellipsoid. Bull. Geodesique 69, 164–172 (1995) Google Scholar Grafarend, E.W., Hendricks, A., Gilbert, A.: Transformation of conformal coordinates of type Gauss-Krueger or UTM from a local datum (re...
Building on work of Hadamard and Volterra, he generalized Banach spaces to use new (non-normed) metrics and proved that many important theorems still applied in these more general spaces. For this work, and his invention of the notion of compactness, Fréchet is called the Founder of the ...
On rational De Rham cohomology associated with the generalized airy function An important related problem is a cohomological interpretation of the integral, i.e., to clarify the structure of the cohomology group of a twisted complex associated to the integral. The author solves this problem in thi...
A generalized way of writing this is g⊲xy =(g (1) ⊲x)(g (2) ⊲y) (1) for all g ∈ U(g), where the coproduct is defined as g (1) ⊗g (2) ≡ ∆(g) := g ⊗1 +1 ⊗g on the generators g ∈g and extended to a homomorphismon the enveloping algebra. ...
In the previous section, we saw that T-duality symmetries relate winding and momentum modes of the string, and for the string on a torus Td the mass spectrum can be covariantly written as M2 = p2 + HMN P MP N + (N + N¯ − 2), (19) where HMN is the generalized metric and...
It will be seen later how this can be generalized for the case of BRST-anti-BRST transformations. If the algebra depends on the last term, i.e., E is not zero, we have an open algebra and an non-nilpotent BRST transformation acting on the initial fields. The gauge fixed action ...