Related papers: Uniqueness and order in sequential effect algebras
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there…
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced order for a natural class of systems of dimension $\geq 2$…
In this paper we characterize finite effect algebras which have a state. We construct two matrices $A$ and $B$ assigned to a finite effect algebra $E$ and show that if $E$ has a state then rank$A=$ rank$B$.
A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a Leibniz rule. If we part from a Lie color algebra, instead of a Lie algebra, a…
Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and the Matrix-Tree Theorem, we give a combinatorial proof that…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We explore asynchronous programming with algebraic effects. We complement their conventional synchronous treatment by showing how to naturally also accommodate asynchrony within them, namely, by decoupling the execution of operation calls…
In the context of commutative differential graded algebras over $\mathbb Q$, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…
We introduce the notions of $\tau$-exceptional and signed $\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between…
We investigate sigma-entangled linear orders and narrowness of Boolean algebras. We show existence of sigma-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the…
In this paper, we show that those sequential products which were proposed by Liu and Shen and Wu in [J. Phys. A: Math. Theor. {\bf 42}, 185206 (2009), J. Phys. A: Math. Theor. {\bf 42}, 345203 (2009)] are just unitary equivalent to the…
We model actors based on truly concurrent process algebra, and capture the actor model in the following characteristics: (1) Concurrency: all actors execute concurrently; (2) Asynchrony: an actor receives and sends messages asynchronously;…
We show that the product of any number of sequentially pseudocompact topological spaces is still sequentially pseudocompact. The definition of sequential pseudocompactness can be given in (at least) two ways: we show their equivalence. Some…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Most existed work require knowledge about the effect of program instructions (or statements) to analyze and verify algorithms. In this paper, by revealing some findings on executions of object programs, we define two basic concepts --…
Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…