A discretized point-hyperplane incidence bound in Rd\mathbb{R}^d

Let $P$ be a $\delta$-separated $(\delta, s, C_P)$-set of points in $B(0, 1)\subset \mathbb{R}^d$ and $\Pi$ be a $\delta$-separated $(\delta, t, C_\Pi)$-set of hyperplanes intersecting $B(0, 1)$ in $\mathbb{R}^d$. Define $$I_{C\delta}(P, \Pi)=\#\{(p, \pi)\in P\times \Pi\colon p\in \pi(C\delta)\}.$$ Suppose that $s, t\ge \frac{d+1}{2}$, then we have $I_{C\delta}(P, \Pi)\lesssim \delta |P||\Pi|$. The main ingredient in our argument is a measure theoretic result due to Eswarathansan, Iosevich, and Taylor (2011) which was proved by using Sobolev bounds for generalized Radon transforms. Our result is essentially sharp, a construction will be provided and discussed in the last section.Comment: 14 page

Discretized sum-product type problems: Energy variants and Applications

In this paper we establish non-trivial estimates for the additive discretized energy of $$\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le \delta\}|_{\delta},$$ that depend on the non-concentration conditions of the sets. Our proofs introduce a number of novel approaches which make use of a combination of methods from both continuous and discrete settings including a pivoting argument, which has been used in the finite field setting due to Murphy and Petridis, the recent Guth-Katz-Zahl's method for the discretized sum-product problem and a Dabrowski-Orponen-Villa point-tube incidence bound. As applications, we obtain a number of improvements on the size of the $\delta$-covering of sets $A + cB$ and $C(A+A)$. Furthermore, for compact sets $A, B\subset \mathbb{R}$, we also prove new explicit upper bounds on the quantity $\dim_H\{c\in \mathbb{R}\colon \dim_H(A+cB)\le \alpha+\epsilon\}$. Our approach leads to considerably shorter proofs over the previous works due to Bourgain and Orponen.Comment: 39 page

BLOCKCHAIN-BASED DISINTERMEDIATION AND ITS EFFECT IN B2C RELATIONSHIP

Objectives To establish a comprehensive understanding of blockchain-based disintermediation and its effect on B2C relationships, the first critical thing to identify is the promising features of blockchain. Then, the concept and usage of disintermediation are investigated. Afterward, the concept of blockchain-based disintermediation and its benefit in B2C relationship building are explored. Finally, this thesis aims to recognize the challenges of using blockchain to enhance B2C relationships in the current phase of blockchain development. Summary Digitalization and the move toward mass customization have vitalized customer data and its impacts in the value chain, which encourage the growth of data intermediaries. However, the dominance of these intermediaries in the processing of data results in data vulnerability, prevents the value maximization of customer data, and threatens B2C relationships. With its technical properties, namely decentralization, security, transparency, and immutability, blockchain can be an optimal solution for this data dilemma. Through blockchain-based solutions, disintermediation, or removal of unnecessary data intermediaries, is encouraged, which can improve the processing of customer data and strengthen B2C relationships. Conclusions Blockchain-encouraged disintermediation can reduce cost, complexity, and uncertainty associated with data intermediaries’ dominance while also redistributing control, adding trust, and improving B2C relationships. Customers might have complete control in a secured data management process, in which they can monetize their data. Simultaneously, B2C firms can directly communicate to their customers, access more accurate customer data, and encourage customers to co-create value

Optimization of ultrasound-assisted extraction of phenolic compounds from fresh Moringa oleifera leaves with a response surface methodology and comparison with the Soxhlet extraction method

ABSTRACT. The present study evaluated the optimum conditions of ultrasound-assisted extraction (UAE) and Soxhlet extraction (SE) of antioxidant capacities and total phenolics from fresh Moringa oleifera leaves, using the response surface methodology. Spectrophotometric method with Folin–Ciocalteu and 2,2-diphenyl-1-picrylhydrazyl (DPPH) reagents was used to determine the total phenolic content (TPC) and the antioxidant activity (AA), respectively. The four models obtained showed the non-linear and quadratic dependences of both measured responses (TPC and AA) which were influenced significantly by all control variables including the acetone solvent (70%, v/v) to solid (SS) ratio, extraction time, and extraction temperature of both extraction methods. Furthermore, at the same extraction temperature, the extraction efficacy of UAE was better than SE as significantly shorter extraction time, less extraction solvent, but higher bio-active content was experienced. The optimal UAE conditions included a SS ratio of 31:1 (mL/g), extraction time of 26 min, and extraction temperature of 59 oC, resulting in the maximum TPC (34.36 mg GAE/g dry weight, DW) and AA (491.9 µmol TE/g DW) in the extracts. In addition, the models proposed were considered to be accurate and reliable for predicting the TPC and AA of fresh M. oleifera leaf extract. The research findings also imply potential applications for ultra-sonication extraction to produce the extracts from fresh M. oleifera leaves for pharmaceutical industry as well as food technology.   KEY WORDS: Antioxidant activity, Herbal plant, Model, Polyphenols, RSM   Bull. Chem. Soc. Ethiop. 2022, 36(2), 261-275.                                                                DOI: https://dx.doi.org/10.4314/bcse.v36i2.