Related papers: On the expressive power of Lukasiewicz's square op…
We consider an extension of bi-intuitionistic logic with the traditional modalities from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with…
Let $c$ be an element of the Weyl algebra $W(d)$ which is given by a strictly positive operator in the Schr"odinger representation. It is shown that, under some conditions, there exist elements $b_1,...,b_d$ in $W(d)$ such that $b_1 c b_1^*…
In this paper, we consider general Markov chains (MC), specified by the transition probability (kernel) $ P (x, E) $, finitely additive in the second argument. Such MC are studied within the framework of the functional operator treatment.…
We introduce a family of modal expansions of {\L}ukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics…
Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy…
A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…
The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory…
Operator square-roots are ubiquitous in theoretical physics. They appear, for example, in the Holstein-Primakoff representation of spin operators and in the Klein-Gordon equation. Often the use of a perturbative expansion is the only…
We characterize the expressive power of the modal mu-calculus on monotone neighborhood structures, in the style of the Janin-Walukiewicz theorem for the standard modal mu-calculus. For this purpose we consider a monadic second-order logic…
This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…
Recently a new family of enumerative invariants called leaky Hurwitz numbers was introduced by Cavalieri-Markwig-Ranganathan in the context of logarithmic intersection theory. They admit an interpretation via tropical covers where the…
Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be…
We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…
In the first part of the paper we defined and studied a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. For type $A$ we conjecture, following Geiss and Schr\"oer, that this operation is…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose…
On L 2 (R), we consider the Schr\"odinger operator (1.1) H \k{o} = -- $\partial$ 2 $\partial$x 2 + v(x) -- \k{o}x, where v is a real analytic 1-periodic function and \k{o} is a positive constant. This operator is a model to study a Bloch…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…