Numerous models have been proposed under the name of structured systems analysis and design. Because of the lack of a common theoretical framework, the transition from one model to another is arbitrary and can only be done manually. An initial algebra approach is proposed to integrate the structured models. The algebra defined can be mapped through homomorphisms to Yourdon structure charts and ...

As an alternative to the classical approach to the compiler correctness problem where a given compiler is proved correct from scratch, we propose a method for deriving correct compilers from a denotational semantics via a series of reenements. Each such optimization step corresponds to an eeciency improvement in the corresponding compiler. Our technique combines the standard initial algebra sem...

For a given configuration space M and Lie algebra G whose action is defined on M the space V 0.0 of weakly G-invariant Lagrangians (i.e. Lagrangians whose motion equations left hand sides are G-invariant) is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex using the m...

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups  including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...

LetA be a finite-dimensional commutative algebra over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the algebra of complex-valued functions on M, with respect to pointwise addition and multiplication of functions, by sending an element x of A to the function on M w...

In this paper, we study the fundamental algorithmic problem of determining the homomorphisms from an Amodule M to an A-module N over an algebra A. We shall outline an algorithm for the case that A is a finite dimensional algebra over a finite field F and both modules M and N are finitely generated as A-modules. More specifically, the input to our algorithm consists of the following data: The mo...

In this paper we establish a direct connection between stable approximate unitary equivalence for ∗-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this to...

We prove that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra O2. We further prove that if A is a simple separable unital nuclear C*-algebra, then O2 ⊗ A ∼= O2, and if, in addition, A is purely infinite, then O∞ ⊗ A ∼= A. The embedding of exact C*-algebras in O2 is continuous in the following sense. If A is a continuous field of C*-algebras over a compact manif...

We introduce an algebra of instruction sequences by presenting a semigroup C in which programs can be represented without directional bias: in terms of the next instruction to be executed, C has both forward and backward instructions and a C-expression can be interpreted starting from any instruction. We provide equations for thread extraction, i.e., C’s program semantics. Then we consider thre...