Search results for "algebra"
showing 10 items of 4129 documents
Interpreting Connexive Principles in Coherence-Based Probability Logic
2021
We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If \(\mathord {\thicksim }A\), then A, should not hold, since the conditional’s antecedent \(\mathord {\thicksim }A\) contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event \(A|\bar{A}\) is \(p(A|\bar{A})=0\). Moreover, connexive logics aim to capture the intuition that conditionals should express some “connection” between the antecedent and the consequent or, in terms of inferences, valid…
Probabilistic squares and hexagons of opposition under coherence
2017
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the set of all coherent assessments on a finite sequence of conditional events. Finally, as an application, we present new versions of the square and of the…
Applications of topological *-algebras of unbounded operators to modified quons
2002
In this paper we discuss some applications of topological *-algebras of unbounded operators to what we call Modified Quons (MQ). In particular, the existence of the thermodynamical limit for some models of free and interacting modified quons is proved in the same framework proposed by the author in a recent paper for ordinary bosons.
States and representations of CQ∗ -algebras
1994
A class of quasi *-algebras which exhibits some analogy with C*-algebras is studied. The extension of some properties of C*-algebras which are relevant for physical applications (such as the GNS-representation) is discussed. Quasi *-algebras of linear operators in rigged Hilbert space are shown to be typical examples of the developed framework.
Computational issues of an electromagnetics transient meshless method
2019
In this paper we refer to the computational issues in solving Maxwell’ s curl equations without using any connectivity among the points in which the problem domain is discretized. The adopted procedure is able to approximate the electric and magnetic vector fields making use of the derivatives of a kernel function at points arranged in the computational domain. In order to improve the numerical accuracy, dealing with irregular data distribution or data located near the boundary, a suitable strategy is considered. The computational core of the overall process requires elementary linear algebra operations. In the paper the method is presented and the discussion is revolved to the computationa…
Inverse procedural modeling of 3D models for virtual worlds
2016
This course presents a collection of state-of-the-art approaches for modeling and editing of 3D models for virtual worlds, simulations, and entertainment, in addition to real-world applications. The first contribution of this course is a coherent review of inverse procedural modeling (IPM) (i.e., proceduralization of provided 3D content). We describe different formulations of the problem as well as solutions based on those formulations. We show that although the IPM framework seems under-constrained, the state-of-the-art solutions actually use simple analogies to convert the problem into a set of fundamental computer science problems, which are then solved by corresponding algorithms or opt…
The associated sheaf functor theorem in algebraic set theory
2008
We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.
Hochschild Cohomology Theories in White Noise Analysis
2008
We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.
On Shimura subvarieties of the Prym locus
2018
We show that families of Pryms of abelian Galois covers of $\mathbb{P}^1$ in $A_{g-1}$ (resp. $A_g$) do not give rise to high dimensional Shimura subvareties.
The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves
2017
Abstract Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g > 7 .