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Leafy vegetables may get contaminated with pathogens through the use of irrigation water during open field cultivation. The main control option to prevent this contamination is the use of disinfection technologies that will reduce the pathogenic load of the irrigation water. Several technologies, either chemical or physical, are available for disinfection, which were gathered from the literature and European Union (EU) projects. The purpose of this paper is to prioritise these technologies.

A feasibility study was performed to identify the most promising disinfection technology considering 12 different criteria. A two-tier approach was used in which the technologies were first evaluated based on three criteria: legal status, effectiveness and technology readiness level (TRL). Only the technologies that reached pre-set thresholds for these three criteria were then evaluated in the second tier.

The evaluation showed that the most promising technologies after the tier-2 evaluation were ultrasound, microfiltration, ultraviolet and ozone. The study showed that the followed approach enabled prioritising disinfection technologies allowing for selecting the most promising technologies that can be tested further on a possible application during primary production to prevent possible food safety issues in leafy vegetables.

The overview is not an exhaustive list of disinfection technologies available rather only those technologies that seemed promising for application in horticulture were addressed. Some technologies may, thus, have been missed. Nevertheless, a total of 12 single and seven combined technologies were evaluated.

This is the first study that uses a structured approach to prioritise a broad range of possible water disinfection technologies for use at primary production.

L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative _d-frame and approximative _d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative _d-Bessel sequence and approximative _d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

In this work, the authors are interested in the notion of vector valued and set valued Pettis integrable pramarts. The notion of pramart is more general than that of martingale. Every martingale is a pramart, but the converse is not generally true.

In this work, the authors present several properties and convergence theorems for Pettis integrable pramarts with convex weakly compact values in a separable Banach space.

The existence of the conditional expectation of Pettis integrable mutifunctions indexed by bounded stopping times is provided. The authors prove the almost sure convergence in Mosco and linear topologies of Pettis integrable pramarts with values in (cwk(E)) the family of convex weakly compact subsets of a separable Banach space.

The purpose of the present paper is to present new properties and various new convergence results for convex weakly compact valued Pettis integrable pramarts in Banach space.

To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.

Develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy‐Kovalevskaya theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray‐Miller theorem based on analytic parameters, and the Banach‐space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of classes of Adomian polynomials, the author develops the novel notion of a sequence of parametrized partial sums as defined by truncation operators, acting upon infinite series, which induce these parametrized sums for simple discard rules and appropriate decomposition parameters. Thus, the defining algorithm of the Adomian polynomials is the difference of these consecutive parametrized partial sums.

The four classes of Adomian polynomials are shown to belong to a common family of decomposition series, which admit solution by recursion, and are derived from one unifying formula. The series of Adomian polynomials and hence the solution as computed as an Adomian decomposition series are shown to be uniformly convergent. Furthermore, the limiting value of the mth Adomian polynomial approaches zero as the index m approaches infinity for the prerequisites of the Cauchy‐Kovalevskaya theorem. The novel truncation operators as governed by discard rules are analogous to an ideal low‐pass filter, where the decomposition parameters represent the cut‐off frequency for rearranging a uniformly convergent series so as to induce the parametrized partial sums.

This paper unifies the notion of the family of Adomian polynomials for solving nonlinear differential equations. Further it presents the new notion of parametrized partial sums as a tool for rearranging a uniformly convergent series. It offers a deeper understanding of the elegant and powerful Adomian decomposition method for solving nonlinear ordinary and partial differential equations, which are of paramount importance in modeling natural phenomena and man‐made device performance parameters.

The fractional order HIV model has an important role in biological science. To study the HIV model in a better way, the model is presented with the help of Atangana- Baleanu operator which is in Caputo sense. Also, the characteristics of the solutions are described briefly with the help of the advance numerical techniques for the different values of fractional order derivatives. This paper aims to discuss the aforementioned objectives.

In this work, Adams-Bashforth method and Euler method are used to get the solution of the HIV model. These are the important numerical methods. The comparison results also are described with the physical meaning of the solutions of the model.

HIV model is analyzed under the view of fractional and AB derivative in Atangana-Baleanu-Caputo sense. The uniqueness of the solution is proved by using Banach Fixed point. The solution is derived with the help of Sumudu transform. Further, the authors employed fractional Adam-Bashforth method and Euler method to enumerate numerical results. The authors have used several values of fractional orders to present the outcomes graphically. The above calculations have been done with the help of MATLAB (R2016a). The numerical scheme used in the proposed study is valid and fruitful, and the same can be used to explore other real issues.

This investigation can be done for the real data sets.

This paper aims to express the solution of the HIV model in a better way with the effect of non-locality, this work is very useful.

In this work, HIV model is developed with the help of Atangana- Baleanu operator in Caputo sense. By using Banach Fixed point, the authors proved that the solution is unique. Also, the solution is presented with the help of Sumudu transform. The behaviors of the solutions are checked for different values of fractional order derivatives with the physical meaning with help of the Adam-Bashforth method and the Euler method.

This paper aims to report on the bibliometric research trends on the application of machine learning/intelligent systems in the prediction of food contamination and the surveillance of foodborne diseases.

In this study, Web of Science (WoS) core collection database was used to retrieve publications from the year 1996–2021. Document types were classified according to country of origin, journals, citation and key research areas. The bibliometric parameters were analyzed using VOSviewer version 1.6.15 to visualize the international collaboration networks, citation density and link strength.

A total of 516 articles across 6 document types were extracted with an average h-index of 51 from 10,570 citations. The leading journal in publications was Science of the Total Environment (3.6%) by Elsevier and the International Journal of Food Microbiology (2.5%). The United States of America (USA) (24%) followed by the People's Republic of China (17.2%) were the most influential countries in terms of publications. The top-cited articles in this study focused on themes such as contamination from packaging materials and on the strategies for preventing chemical contaminants in the food chain.

This report is significant because the public health field requires innovative strategies in forecasting foodborne disease outbreaks to advance effective interventions. Therefore, more collaboration need to be fostered, especially in developing nations regarding food safety research.

This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.

A generalization of Ascoli–Arzelá theorem in Banach spaces is established. Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order. The authors’ results are obtained under, rather, general assumptions.

First, a generalization of Ascoli–Arzelá theorem in Banach spaces in Cⁿ is established. Second, this new generalization with Schauder's fixed point theorem to prove the existence of a solution for a boundary value problem of higher order is used. Finally, an illustrated example is given.

There is no funding.

In this work, a new generalization of Ascoli–Arzelá theorem in Banach spaces in Cⁿ is established. To the best of the authors’ knowledge, Ascoli–Arzelá theorem is given only in Banach spaces of continuous functions. In the second part, this new generalization with Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order, where the derivatives appear in the non-linear terms.

In this paper, we study a Cauchy-type problem for Hilfer fractional integrodifferential equations with boundary conditions. The existence of solutions for the given problem is proved by applying measure of noncompactness technique in an abstract weighted space. Moreover, we use generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of ϵ-approximate solutions.

In this paper the aim is to present some subspace simultaneously proximinal in the Banach space L₁(μ, X) of X‐valued Bochner μ‐integrable functions.

By lower semicontinuity and compactness the existence of best simultaneous approximation is obtained.

If Y is a reflexive subspace of a Banach space X, then L₁(μ, Y) is simultaneously proximinal in L₁(μ, X). Furthermore, if X is reflexive and μ₀ is the restriction of μ to a sub‐σ‐algebra, then L₁(μ₀, X) is simultaneously proximinal in L₁(μ, X).

Given a finite number of points in the Banach space X, is about finding a point in the subspace Y⊂X that comes close to all this points.

By the property of reflexivity two types subspaces simultaneously proximinal in L₁(μ, X) are obtained.