In this work we develop and examine a generalized account of David Lewis’s imaging in the same way as how Jeffrey’s Probability Kinematics generalizes Bayesian conditionalization. We show that this naturally leads to a rational account of probabilistic belief removal – a rather long standing problem in the area. It turns out that our generalization of imaging indeed is an account of probabilist...

Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

and Applied Analysis 3 Definition 2.3 see 16 . Let X,F, T be a probabilistic metric space. A mapping f : X → X is said to be a Sehgal contraction or B-contraction if the following relation holds: Ff p f q kt ≥ Fpq t , ( p, q ∈ X, t > 0. 2.1 Theorem 2.4 see 17 . Let X,F, T be a complete probabilistic metric space with T of Hadžić-type and f : X → X be a B-contraction. Then f has a fixed point if...

Probabilistic numerical methods aim to model numerical error as a source of epistemic uncertainty that is subject to probabilistic analysis and reasoning, enabling the principled propagation of numerical uncertainty through a computational pipeline. In this paper we focus on numerical methods for integration. We present probabilistic (Bayesian) versions of both Markov chain and Quasi Monte Carl...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...