Convex-Cyclic Weighted Translations On Locally Compact Groups

A bounded linear operator $T$ on a Banach space $X$ is called a convex-cyclic operator if there exists a vector $x \in X$ such that the convex hull of $Orb(T, x)$ is dense in $X$. In this paper, for given an aperiodic element $g$ in a locally compact group $G$, we give some sufficient conditions for a weighted translation operator $T_{g,w}: f \mapsto w\cdot f*\delta_g$ on $\mathfrak{L}^{p}(G)$ to be convex-cyclic. A necessary condition is also studied. At the end, to explain the obtained results, some examples are given

On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

Let be a locally compact group with a fixed left Haar measure and Ω be a system of weights on . In this paper, we deal with locally convex space (,Ω) equipped with the locally convex topology generated by the family of norms (‖.‖,)∈Ω. We study various algebraic and topological properties of the locally convex space (,Ω). In particular, we characterize its dual space and show that it is a semireflexive space. Finally, we give some conditions under which (,Ω) with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum

Porosity of certain subsets of Lebesgue spaces on locally compact groups

Let $G$ be a locally compact group. In this paper, we show that if $G$ is a non-discrete locally compact group, $p\in(0,1)$ and $q\in(0,+\infty]$, then the set of all pairs $(f, g)\in L^p(G)\times L^q(G)$ for which $f\ast g$ is finite, forms a set of first category in $L^p(G)\times L^q(G)$. 10.1017/S000497271200094

Topologically transitive sequence of cosine operators on Orlicz spaces

For a Young function phi and a locally compact second countable group G, let L phi (G) denote the Orlicz space onG. In this paper, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators {Cn}n=1 infinity:={12(Tg,wn+Sg,wn)}n=1 infinity, defined on L phi (G). We investigate the conditions for a sequence of cosine operators to be topologically mixing. Further, we go on to prove a similar result for the direct sum of a sequence of cosine operators. Finally, we give an example of topologically transitive sequence of cosine operators

Predictive modeling of oleuropein release from double nanoemulsions: An analytical study comparing intelligent models and Monte Carlo simulation

The objective of this study was to evaluate the release of oleuropein (OLP) from double nanoemulsions stabilized with polymeric complexes. Initially, W1/O nano-emulsions loaded with OLP were prepared and re-emulsified into an aqueous phase (W2), which included a complex of whey protein concentrate (WPC)/pectin, to form W1/O/W2 emulsions. The microstructure of the final double emulsions was analyzed by scanning electron microscopy (SEM), and particles with smooth, comparatively spherical, and somewhat asymmetrical surfaces with a size range of 100–200 nm were observed, which were compatible with dynamic light scattering (DLS) data. The release trend of OLP was determined by fitting it to several empirical models including zero order, first order, Higuchi, Hixson-Crowell, Korsemeyer-Peppas, Baker-Lonsdale, and utilizing intelligent modeling techniques such as Fuzzy Logic (FL) and Artificial Neural Networks (ANNs). Among the mathematical models, the zero order equation had the highest coefficient of determination (R2 = 0.988), while the first order equation had the lowest root-mean-square error (RMSE = 0.0176) and sum of squared errors (SSE = 0.0009) for the goodness of fit of the model, when considering the release trend of OLP. FL and ANNs proved effective in modeling controlled release of OLP-loaded nanocarriers, achieving high R2 values. Additionally, Monte Carlo (MC) simulation showed potential for evaluating the release process when compared to other methods

Bishop’s property (β) and weighted conditional type operators in k-quasi class A*n

An operator T is said to be k-quasi class A*n operator if T*ᵏ (|Tⁿ⁺¹|²/ⁿ⁺¹− |T*|² ) Tᵏ ≥ 0, for some positive integers n and k. In this paper, we prove that the k-quasi class A*n operators have Bishop, s property (β). Then, we give a necessary and sufficient condition for T ⊗S to be a k-quasi class A*n operator, whenever T and S are both non-zero operators. Moreover, it is shown that the Riesz idempotent for a non-zero isolated point λ0 of a k-quasi class A*n operator T say Rᵢ, is self-adjoint and ran(Rᵢ) = ker(T −λ₀) = ker(T −λ₀)*. Finally, as an application in the last section, a necessary and sufficient condition is given in such a way that the weighted conditional type operators on L² (Σ), defined by Tw,u(f) := wE(uf), belong to k-quasi- A*n class.Publisher's Versio

Porous sets and lineability of continuous functions on locally compact groups

Let G be a non-compact locally compact group. In this paper we study the size of the set {(f, g) is an element of A x B : f * g is well-defined on G} where A and B are normed spaces of continuous functions on G. We also consider the problem of the spaceability of the set (C-0 (G) boolean AND (C-0(G) * C-0(G))) \ C-00 (G) and (among other results) we show that, for G = R-n, the above set is strongly c-algebrable (and, therefore, algebrable and lineable) with respect to the convolution product