A major part of this paper is devoted to an in-depth study j -operators and their properties. This enables us obtain several results on liftings weak DG modules along simple extensions algebras unify the proofs existing obtained by authors these subjects. Finally, we provide a new characterization (weak) lifting property algebras.

We define a general condition, called stability on extensions T of measure preserving transformations S . Stability is defined in terms of relative unique ergodicity, and as a joining property. Ergodic compact group extensions are stable, and moreover stable extensions satisfy lifting theorems similar to those satisfied by group extensions. In general, stable extensions have relative entropy ze...

We study the construction of preorders on Set-monads by the semantic ⊤⊤-lifting. We show the universal property of this construction, and characterise the class of preorders on a monad as a limit of a Card-chain. We apply these theoretical results to identifying preorders on some concrete monads, including the powerset monad, maybe monad, and their composite monad. We also relate the constructi...

In this paper we connect the design of biorthogonal modulated filter banks with the idea of lifting schemes, which were proposed for the construction of biorthogonal wavelets. Based on this formulation, we derive a lattice-like structure for the polyphase components. As the rotationbased structures for the design and implementation of paraunitary modulated filter banks, our structure automatica...

The core of the mathematical development in this paper consists of lifting the — categorically — equivalent descriptions of physical systems by a (i) ‘state space’ or a (ii) ‘property lattice’ — see [14,20,25,26] — to an asymmetrical — i.e., not anymore isomorphic — duality on the level of: (i) ‘possible state’ transitions — ‘possible’ in the sense that an arbitrary initial state is mapped onto...

In this paper a novel algorithm for robust video watermarking in image using orthogonal wavelet transform (HAAR) and bi-orthogonal (Daubechies Lifting) based on an image texture is described. To embed the watermark, property of texture (rough area) is used as a measure to find actual target area. Watermark is embedded into LL sub-band as it is having highest texture. Image’s distortion is reduc...

In this paper, a new lifting wavelet domain audio watermarking algorithm based on the statistical characteristics of sub-band coefficients is proposed. First of all, an original audio signal was segmented and each segment was divided into two sections. Then, the Barker code was used for synchronization, the LWT (lifting wavelet transform) was performed on each section, a synchronization code an...

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition, product, pullback, retract, and limits of towers; see Lemma C.1.1. Proof. For now see [17, 11.1.4] and dualize. On account of the dual of Lemma C.1.1, any set of maps in a cocomplete category “cellularly g...

We give a criterion for when idempotents of a ring R which commute modulo the Jacobson radical J(R) can be lifted to commuting idempotents of R. If such lifting is possible, we give extra information about the lifts. A “half-commuting” analogue is also proven, and this is used to give sufficient conditions for a ring to have the internal exchange property. In particular, we show that if R/J(R) ...

Abstract Sarnak’s density conjecture is an explicit bound on the multiplicities of nontempered representations in a sequence cocompact congruence arithmetic lattices semisimple Lie group, which motivated by work Sarnak and Xue ([58]). The goal this to discuss similar hypotheses, their interrelation applications. We mainly focus two properties – spectral spherical hypothesis geometric Weak injec...