It is widely acknowledged that users are important actors in innovation projects: the market success of new products and services depends highly on addressing customer requirements without overloading them with too many new features and technologies (Lettl/Gemünden 2005; Mason/Harris 2005). Going beyond traditional market research and integrating customers intensively into the innovation proces...

We consider a general formulation for shape optimization problems involving the eigenvalues of the Laplace operator. Both the cases of Dirichlet and Neumann conditions on the free boundary are studied. We survey the most recent results concerning the existence of optimal domains, and list some conjectures and open problems. Some open problems are supported by efficient numerical computations.

In his seminal work [Plaza, 1989], Plaza proposed the public announcement logic (PAL), which is considered as the pilot logic in the field of dynamic epistemic logic. In the same paper, Plaza also introduced an interesting “know-value” operator Kv and listed a few valid formulas of PAL+Kv. However, it is unknown that whether these formulas, on top of the axioms for PAL, completely axiomatize PA...

We study open and closed string interactions in the Type IIB plane wave background using open+closed string field theory. We reproduce all string amplitudes from the dual N = 2 Sp(N) gauge theory by computing matrix elements of the dilatation operator. A direct diagrammatic correspondence is found between string theory and gauge theory Feynman diagrams. The prefactor and Neumann matrices of ope...

The mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more “natural”. But for the developer, the richness leads to syntactic complexity, such as dealing with overloading. As part of the larger project of open-sourcing the mizar codebase, the m...

We present a formal approach for modeling complex commands characterized by heavy overloading of function, large numbers of parameters, dependencies among parameters, subtle side effects, and lack of abstraction. Complex commands arise in a variety of business settings such as requesting a brokerage order, enrolling in a course, and specifying a product order. In addition, complex commands are ...

We derive explicit formulas for the eigenvalues and eigenvectors of the Discrete Laplacian on a rectangular grid for the standard finite difference and finite element methods in 1D, 2D, and 3D. Periodic, Dirichlet, Neumann, and mixed boundary conditions are all considered. We show how the higher dimensional operators can be written as sums of tensor products of one dimensional operators, and th...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

SPPF (shared packed parse forest) is the best known graph representation of a parse forest (family of related parse trees) used in parsing with ambiguous/conjunctive grammars. Systematic general purpose transformations of SPPFs have never been investigated and are considered to be an open problem in software language engineering. In this paper, we motivate the necessity of having a transformati...

We examine the relationship between the decoherence of quantummechanical histories of a closed system (as discussed by Gell-Mann and Hartle) and environmentally-induced diagonalization of the density operator for an open system. We study a definition of decoherence which incorporates both of these ideas, and show that it leads to a consistent probabilistic interpretation of the reduced density ...