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We address the general classification problem of all stable associative product structures in the complex cobordism theory. We show how to reduce this problem to the algebraic one in terms of the Hopf algebra $S$ (the Landweber-Novikov…
We study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects…
The Rankin--Cohen brackets provide a basic example of ``non-elementary" differential symmetry breaking operators. They can be interpreted as bi-differential operators remarkable for reflecting the structure of fusion rules for holomorphic…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN-pair, with respect to a…
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the H\"ormander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise…
The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…
In this article we show how the data of integrals of algebraic differential forms over algebraic cycles can be used in order to prove that algebraic and Hodge cycle deformations of a given algebraic cycle are equivalent. As an example, we…
We revisit hierarchical bracketing encodings from a practical perspective in the context of dependency graph parsing. The approach encodes graphs as sequences, enabling linear-time parsing with $n$ tagging actions, and still representing…
It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
The paper "Sorting with Bialgebras and Distributive Laws" by Hinze et al. uses the framework of bialgebraic semantics to define sorting algorithms. From distributive laws between functors they construct pairs of sorting algorithms using…
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical…
A new modeling framework for bipartite social networks arising from a sequence of partially time-ordered relational events is proposed. We directly model the joint distribution of the binary variables indicating if each single actor is…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
An explicit lattice realization of a non-Abelian topological memory is presented. The correspondence between logical and physical states is seen directly by use of the stabilizer formalism. The resilience of the encoded states against…