Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, paths related objects with a quantified singularity at zero. In pure path setting this allows us to leverage on existing SLE Besov estimates see that traces takes values H\"older space, which quantifies well-known boundary effect regime $\kappa < ...

We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11 (1983) 46–57]. This condition is verified in many examples, even in absence of explicit expressions for the covariance or Volterra kernels. Of special interest are ran...

The objective of this study was to determine effect of germination on total anthocyanin content (TAC) and antioxidant activity of colored rice (Oryza sativa L). The normal, non-waxy rice variety Phitsanulok 2 was used as a control and two pigmented rice including black glutinous rice (local name Niew Dam), and black non-waxy rice (local name Hom Nil) were used in this study. Rough rice and dehu...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

In this paper, we study the boundedness theory for maximal Calderón–Zygmund operators acting on noncommutative $$L_p$$ -spaces. Our first result is a criterion weak type (1, 1) estimate of operators; as an application, obtain estimates operator-valued singular integrals convolution under proper regularity conditions. These are inequalities families truly non-positive linear operators. For homog...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...