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15 pages, 296 KiB

Open AccessArticle

On Some Multipliers Related to Discrete Fractional Integrals

by Jinhua Cheng

Mathematics 2024, 12(10), 1545; https://doi.org/10.3390/math12101545 - 15 May 2024

Viewed by 1305

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler’s identity, and Dedekind zeta functions of quadratic imaginary fields. Employing Fourier transform techniques, the Hardy–Littlewood circle method, and a discrete analogue of [...] Read more.

ℓ^{p} \to ℓ^{q}

bounds for these operators. Our results contribute to a deeper understanding of the intricate relationship between number theory and harmonic analysis in discrete domains, offering insights into the convergence behavior of these operators. Full article

(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)

16 pages, 2159 KiB

Open AccessArticle

Biology and Ecology of Delia planipalpis (Stein) (Diptera: Anthomyiidae), an Emerging Pest of Broccoli in Mexico

by Guadalupe Córdova-García, Laura Navarro-de-la-Fuente, Diana Pérez-Staples, Trevor Williams and Rodrigo Lasa

Insects 2023, 14(7), 659; https://doi.org/10.3390/insects14070659 - 24 Jul 2023

Cited by 4 | Viewed by 2298

Abstract

Delia planipalpis (Stein) (Diptera: Anthomyiidae) is a pest of crucifers, such as broccoli, radish, cauliflower, turnip and cabbage. It has been recently described in Mexico as a significant emerging pest of broccoli. Due the lack of knowledge of this pest, the present study aimed to determine its life cycle, female sexual maturation, copulation, oviposition behavior and adult longevity. The identity of the fly in Mexico was confirmed genetically by sequencing the cytochrome oxidase subunit 1 gene (COI). The mean development time of D. planipalpis was 32–33 days on radish at 24 °C under laboratory conditions. Females became sexually mature 1–2 days after emergence, and the highest incidence of matings was recorded on the second day (60%). Under choice conditions, D. planipalpis females preferred to oviposit on radish plants, rather than broccoli plants, possibly due to the use of radish for rearing the laboratory colony. Oviposition and the mean number of eggs laid varied among the broccoli varieties, with the highest oviposition observed on the Tlaloc variety. Repeated attempts to rear the laboratory colony on broccoli plants failed. Radish-reared insects of both sexes lived longer when individualized in the adult stage (14.5–22.5 days) than when adult flies were maintained in groups (10–11 days). This study contributes to the understanding of D. planipalpis biology and provides information that can be used to establish future control strategies against this pest. Full article

(This article belongs to the Section Insect Physiology, Reproduction and Development)

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19 pages, 345 KiB

Open AccessArticle

A Strong Limit Theorem of the Largest Entries of a Sample Correlation Matrices under a Strong Mixing Assumption

by Haozhu Zhao and Yong Zhang

Axioms 2023, 12(7), 657; https://doi.org/10.3390/axioms12070657 - 2 Jul 2023

Cited by 1 | Viewed by 1251

Abstract

We are interested in an n by p matrix

X_{n}

where the n rows are strictly stationary

α

-mixing random vectors and each of the p columns is an independent and identically distributed random vector;

p = p_{n}

goes to infinity [...] Read more.

We are interested in an n by p matrix

X_{n}

where the n rows are strictly stationary

α

-mixing random vectors and each of the p columns is an independent and identically distributed random vector;

p = p_{n}

goes to infinity as

n \to \infty

, satisfiying

0 < c_{1} \leq p_{n} / n^{τ} \leq c_{2} < \infty

, where

τ > 0

c_{2} \geq c_{1} > 0

. We obtain a logarithmic law of

L_{n} = {max}_{1 \leq i < j \leq p_{n}} | ρ_{i j} |

using the Chen–Stein Poisson approximation method, where

ρ_{i j}

denotes the sample correlation coefficient between the ith column and the jth column of

X_{n}

. Full article

(This article belongs to the Special Issue Probability, Statistics and Estimation)

13 pages, 1180 KiB

Open AccessArticle

Variational Inference for a Recommendation System in IoT Networks Based on Stein’s Identity

by Jia Liu, Yuanfang Chen, Sardar M. N. Islam and Muhammad Alam

Appl. Sci. 2022, 12(4), 1816; https://doi.org/10.3390/app12041816 - 10 Feb 2022

Cited by 2 | Viewed by 1650

Abstract

The recommendation services are critical for IoT since they provide interconnection between various devices and services. In order to make Internet searching convenient and useful, algorithms must be developed that overcome the shortcomings of existing online recommendation systems. Therefore, a novel Stein Variational Recommendation System algorithm (SVRS) is proposed, developed, implemented and tested in this paper in order to address the long-standing recommendation problem. With Stein’s identity, SVRS is able to calculate the feature vectors of users and ratings it has generated, as well as infer the preference for users who have not rated certain items. It has the advantages of low complexity, scalability, as well as providing insights into the formation of ratings. A set of experimental results revealed that SVRS performed better than other types of recommendation methods in root mean square error (RMSE) and mean absolute error (MAE). Full article

(This article belongs to the Section Electrical, Electronics and Communications Engineering)

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21 pages, 375 KiB

Open AccessArticle

A Generalized Equilibrium Transform with Application to Error Bounds in the Rényi Theorem with No Support Constraints

by Irina Shevtsova and Mikhail Tselishchev

Mathematics 2020, 8(4), 577; https://doi.org/10.3390/math8040577 - 13 Apr 2020

Cited by 8 | Viewed by 2952

Abstract

We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties. In particular, we prove an optimal moment-type inequality for the Kantorovich distance between a distribution and its equilibrium transform. Using the introduced transform and Stein’s method, we investigate the rate of convergence in the Rényi theorem for the distributions of geometric sums of independent random variables with identical nonzero means and finite second moments without any constraints on their supports. We derive an upper bound for the Kantorovich distance between the normalized geometric random sum and the exponential distribution which has exact order of smallness as the expectation of the geometric number of summands tends to infinity. Moreover, we introduce the so-called asymptotically best constant and present its lower bound yielding the one for the Kantorovich distance under consideration. As a concluding remark, we provide an extension of the obtained estimates of the accuracy of the exponential approximation to non-geometric random sums of independent random variables with non-identical nonzero means. Full article

(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)

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