The notion of an effect algebra was presented by Foulis and Bennett in (Foulis, Bennett, [3] 1994). The definition was motivated by giving an algebraic description of a logic of quantum effects E(H), i.e. the set of all positive self-adjoint operators between zero and identity operator I in a separable complex Hilbert space H. On E(H) was defined a partial operation A ⊕ B = A + B iff A + B ≤ I ...

Let A be a linear bounded operator in a Hilbert space H, N(A) and R(A) its null-space and range, and A∗ its adjoint. The operator A is called Fredholm iff dim N(A) = dim N(A∗) := n < ∞ and R(A) and R(A∗) are closed subspaces of H. A simple and short proof is given of the following known result: A is Fredholm iff A = B + F , where B is an isomorphism and F is a finite-rank operator. The proof co...

In a previous paper [K1] I have constructed a compactification KGLn of the general linear group GLn, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G = GLn × GLn on this compactification. In this paper we show how the space of global section of an arb...

The classical Cayley map, X → (In − X)(In + X) −1 , is a birational iso-morphism between the special orthogonal group SOn and its Lie algebra son, which is SOn-equivariant with respect to the conjugating and adjoint actions respectively. We ask whether or not maps with these properties can be constructed for other algebraic groups. We show that the answer is usually " no " , with a few exceptio...

Let A be the category of unital C∗-algebras. A counterexample is given to show that the unitary group functor U : A −→ Grp (and hence the composite of the forgetful functor G : Grp −→ Set with U) although being a faithful right adjoint, fails to be algebraic even in the commutative case. In so doing, a canonical presentation of any unital C∗-algebra as a quotient of a free product of copies (i....

Let EG be a holomorphic principal G–bundle over a compact connected Riemann surface, where G is a connected reductive affine algebraic group defined over C, such that EG admits a holomorphic connection. Take any β ∈ H(X, ad(EG)), where ad(EG) is the adjoint vector bundle for EG, such that the conjugacy class β(x) ∈ g/G, x ∈ X , is independent of x. We give a sufficient condition for the existen...

To solve a sparse linear system of equations resulting from the finite element approximation of elliptic self-adjoint second order boundary value problems an algebraic multilevel iteration method is presented. The new method can be considered as an extension of methods, which have been defined by Axelsson and Eijkhout [4] for nine-point matrices and later generalized by Axelsson and Neytcheva [...

We are interested in simulation and optimization of gas transport in networks. Different regions of the network may be modelled by different equations: There are three models based on the Euler equations that describe the gas flow in pipelines qualitatively different: a nonlinear model, a semilinear model and a stationary also called algebraic model. For the whole network, adequate initial and ...

Starting from the generalized Konishi anomaly equations at the non-perturbative level, we demonstrate that the algebraic consistency of the quantum chiral ring of the N = 1 super Yang-Mills theory with gauge group U(N), one adjoint chiral superfield X and Nf ≤ 2N flavours of quarks implies that the periods of the meromorphic one-form Tr dz z−X must be quantized. This shows in particular that id...

The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...