Academic literature on the topic 'Absorbing lemma'

We use classical Galerkin approximations, the generalized Aubin–Lions Lemma as well as the Bellman–Gronwall Lemma to study the asymptotical behavior of a two-dimensional fractional Navier–Stokes equation with variable delay. By modifying the fractional Halanay inequality and the comparison principle, we investigate the dissipativity of the corresponding system, namely, we obtain the existence of global absorbing set. Besides, some available results are improved in this work. The existence of a global attracting set is still an open problem.

The concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the end, we will present a very important equivalent of our concept with the rest of the concepts presented previously.

We present a new method for investigating the Lp-type pullback attractors (2 ≤ p < ∞) of a semilinear heat equation on a time-varying domain under quite general assumptions on the nonlinear and forcing terms. The existing approach does not appear applicable here as it is impossible to show the existence of a pullback absorbing set in Lp space when p is large. A new asymptotic decomposition scheme for a non-autonomous pullback attractor has been introduced. The abstract results and preliminary lemmas are also of independent interest and applicable to other systems.

The article describes the unique properties of algae to intensively build up biomass and accumulate the mineral elements present in it from the water environment, the justification of the direction of research on the sorption capacity of freshwater and marine algae, the scheme of the experiment, used materials and methods are described. The study of the sorption capacity of the freshwater algae Lemna minor was carried out in a vivarium under 24-hour lighting using fluorescent lamps, the ambient temperature was 28-30 °C, the air humidity was 75-80%, the temperature of the lake water in glass containers varied between 22-25 ºС. An equal mass of freshwater algae Lemna minor was placed in the prepared water medium with different concentrations of iodine in the form of potassium iodide. The content of iodine in wet and dry algae biomass was determined at the beginning of the experiment, after 15 days and at the end of the experiment. To obtain dry biomass, test samples with different concentrations of iodine were dried at a temperature of 85 ºС. To determine the content of iodine in watercress biomass, the capillary electrophoresis method was used using the Kapel-105M capillary electrophoresis system with a negative polarity high voltage source. In the course of the experiment, a significant increase in the iodine content in the dry biomass of Lemna minor was noted both after 15 days of cultivation and at the end of the experiment. Based on the results of studies of the sorption capacity of the biomass of the freshwater algae Lemna minor according to the level of iodine accumulation, the ability of this algae to accumulate iodine content in its biomass, depending on the concentration of iodine in the cultivation medium, was established. The highest intensity of iodine accumulation in duckweed biomass was noted when it was grown on cultivation media with an iodine concentration of 40-2000 mg/dm3. High concentrations of Iodine in the culture medium had a negative effect on the sorption properties of Lemna minor, accumulation of Iodine in it, delayed growth, and by the end of the experiment caused its death.

Water pollution due to heavy metals has become a serious environmental concern due to their hazardous properties. Since conventional water remediation techniques are generally ineffective and non-environmentally friendly, phytoremediation has gained increasing attention from worldwide researchers and scientists due to its cost-effectiveness and environmental friendliness. Hence, this review first discussed soil and water remediations. Phytoremediation can be divided into five techniques to remove heavy metals from the polluted environment, namely, phytostabilization (phytosequestration), phytodegradation (phytotransformation), phytofiltration (rhizofiltration), phytoextraction (phytoaccumulation), and phytovolatilization. Four common floating aquatic plants (accumulator plants), such as duckweed (Lemna minor), water lettuce (Pistia stratiotes), water hyacinth (Eichhornia crassipes), and watermoss (Salvinia) were discussed in detail due to their great capability in absorbing the metal ions by their roots and further translocating the metal ions to the aerial parts. Furthermore, the parameter studies, such as optimum pH and temperature of the water, exposure duration, initial metal concentration, water salinity, and the addition of chelating agents, were evaluated. The absorption kinetics of the plants was discussed in detail. In short, phytoremediation is a promising green and sustainable water remediation approach. However, further research is necessary to enhance its practicability and performance at large-scale implementation.

The effects of two aquatic plants, duckweed (Lemna sp.) and azolla (Azolla sp.), on the growth performance of fantail goldfish (Carassius auratus) and dissolved nutrient concentrations were studied. The experiments were carried out in triplicate sets over a period of seven weeks. Eight specimens of fantail goldfish (length = 5.16 ± 0.06 cm; body weight = 2.30 ± 0.06 g) were released into each of the aquariums containing 40 L of water. Submerged sponge filters were used as the substrate (bed) for the nitrifying bacteria to facilitate nitrification. The fish were provided feed at the rate of 2% of their body weight twice daily. In situ and ex situ water parameters (temperature, dissolved oxygen, pH, total suspended solids, ammonia, nitrite, nitrate, and phosphate), body weight and length of the Fantail goldfish, and wet weight of aquatic plants were measured weekly. The results showed no significant differences (p > 0.05) in any of the three aquariums in water temperature, pH, and dissolved oxygen. Survival of the fish was 100%. The highest food conversion ratio and specific growth rate were observed in the aquarium stocked with duckweed, followed by the aquarium with azolla and the control set (p < 0.05). The concentrations of nutrients (ammonia and nitrate) were recorded lowest (p < 0.05) in the aquarium with azolla, followed by duckweed and the control. The results suggested that aquatic plants were effective in absorbing nutrients and can serve as biofilters to create better conditions for the growth of the fantail goldfish.

<p class="NoParagraphStyle" align="center"><strong>ABSTRACT</strong></p><p class="NoParagraphStyle" align="center"><strong> </strong></p><p class="NoParagraphStyle">The wasted from feed and feces containt nitrogen and phosphorus can decreased fertility and feability water quality. <em>Lemna perpusilla</em> (duckweed) is prospective to use as an agent of phytoremediation of organic waste and can used as animal feed because it has high protein content. Meanwhile water salinity could be accelerate the growth of giant gourami. The aim of this research was to analyze the ability of <em>L. perpusilla</em> in absorbing nutrients nitrogen and phosphorus in water salinity of 3 ppt. The research was conducted four treatments and three replications. The treatments were A (<em>L. perpusilla</em> and 3 ppt salinity), B (<em>L. perpusilla</em>, 3 ppt salinity and filter), C (<em>L. perpusilla</em>, 3 ppt salinity and aeration), and D (<em>L. perpusilla</em>, 3 ppt salinity, filter and aeration). Experiment were carried in aquaria 50×33×50 cm³ in size with density of gourami fish 150/49.5 L for one month. The results showed that the ability of <em>L. perpusilla</em> to absorb N and P decreased from the beginning of the study due to lack of nutrient source of N and P in the aquaculture media, but increased because the impact of the feeding and metabolism of the gourami. There was no different treatment effect for decreased N and P (P&gt; 0.05). The highest nitrite level was found in D treatment, it means that <em>L. perpusilla</em> not be able to absorb N and P in the media 3 ppt salinity. However, the addition of 3 ppt salinity gives the best results for the survival rate and feed efficiency ratio.</p><p class="NoParagraphStyle"> </p><p class="NoParagraphStyle">Keywords: phytoremediation, <em>Lemna perpusilla</em>, giant gourami fish, nitrogen and phosphorus</p><p class="NoParagraphStyle"> </p><p class="NoParagraphStyle" align="center"><strong> </strong></p><p class="NoParagraphStyle" align="center"><strong>ABSTRAK</strong></p><p class="NoParagraphStyle" align="center"><strong> </strong></p><p class="NoParagraphStyle">Limbah pakan dan feses yang mengandung nitrogen dan fosfor dapat menyebabkan penurunan kesuburan dan kelayakan kualitas air.<em> Lemna perpusilla</em> (<em>duckweed</em>) baik digunakan sebagai agen fitoremediasi organik untuk limbah dan dapat digunakan sebagai pakan hewan karena mengandung protein yang tinggi, sementara media bersalinitas mampu mempercepat pertumbuhan ikan gurami. Tujuan dari penelitian ini adalah untuk menganalisis kemampuan <em>L. perpusilla</em> dalam mengabsorbsi nutrisi nitrogen dan fosfor pada air bersalinitas 3 ppt. Penelitian ini terdiri atas lima perlakuan dan tiga ulangan. Perlakuan yang diberikan adalah A (<em>L. perpusilla</em> dan salinitas 3 ppt), B (<em>L. perpusilla</em>, salinitas 3 ppt dan filter), C (<em>L. perpusilla</em>, salinitas 3 ppt dan aerasi), dan D (<em>L. perpusilla</em>, salinitas 3 ppt, aerasi dan filter). Akuarium yang digunakan berukuran 50×33×50 cm³ dengan kepadatan ikan gurami 150 ekor/49,5 L dan waktu pemeliharaan selama satu bulan. Hasil penelitian ini menunjukkan bahwa kemampuan <em>L. perpusilla</em> menyerap limbah N dan P berkurang dari awal penelitian karena kurangnya sumber nutrisi N dan P pada media pemeliharaan, namun beranjak meningkat yang berdampak dari adanya pemberian pakan dan sisa metabolisme dari ikan gurame. Tidak ada perlakuan yang berpengaruh terhadap pengurangan N dan P (P&gt;0,05). Nilai nitrit tertinggi terdapat pada perlakuan D, hal ini berarti bahwa <em>L. perpusilla</em> tidak mampu untuk menyerap limbah N dan P pada media bersalinitas 3 ppt. Namun penambahan salinitas 3 ppt memberikan hasil yang terbaik bagi derajat kelangsungan hidup ikan gurami dan efisiensi pakan.</p><p class="NoParagraphStyle"> </p><p class="NoParagraphStyle">Kata kunci: fitoremediasi, <em>Lemna perpusilla</em>, ikan gurami, nitrogen dan fosfor</p><p> </p>

In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and weakly $ (k,n) $-absorbing primary hyperideals of a Krasner $ (m,n) $-hyperring, including $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Therefore, we give generalizations of $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Also, we examine the relations between classical hyperideals and the new hyperideals and explore some ways to connect them. Additionally, some main results and examples are given to explain the structures of these concepts. Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.

Étant donné un k-graph (hypergraphe k-uniforme) F, la densité de Turán π(F) de F est la densité maximale parmi tous les k-graphes F-libres. Déterminer π(F) pour un k-graph donné F est un problème extrémal classique. Étant donnés deux k-graphes F et H, un F-facteur de H est une collection de copies de F disjointes sur les sommets de H qui couvrent ensemble tous les sommets de H. Les problèmes de F-facteurs, en tant que renforcement du problème de Turán, visent à trouver des conditions extrémales sur H garantissant un F-facteur, ce qui a également une histoire longue et profonde. Dans cette thèse, nous utilisons de nombreux outils puissants, dont la méthode probabiliste, la méthode de régularité des hypergraphes et la méthode d'absorption, pour étudier les densités de Turán et les F-facteurs de k-graphes F donnés dans des hypergraphes uniformément denses. Contrairement aux graphes, nous savons tous qu'il existe plusieurs notions non équivalentes de quasi-aléatoire dans les k-graphes pour k ≥ 3. Par conséquent, notre travail propose également plusieurs définitions non équivalentes de k-graphes uniformément denses. En gros, un k-graphe H est (d, μ, ⋆)-dense signifie qu'il est d-dense et ⋆-quasi-aléatoire pour une petite valeur de μ > 0 par rapport à des structures aléatoires données. En se limitant aux 3-graphes (d, μ, 1)-dense, la densité de Turán d'un 3-graphe donné F est notée π1(F). La détermination de π1(F) a été suggérée par Erdős et Sós dans les années 1980. En 2018, Reiher, Rödl et Schacht ont étendu le concept de 3-graphes (d, μ, 1)-dense à des k-graphes (d, μ, k-2)-dense pour k ≥ 3, et ils ont proposé l'étude de la densité de Turán uniforme πk-2(F) pour un k-graphe donné F dans des k-graphes (d, μ, k-2)-dense. En particulier, ils ont montré que πk-2(•) saute de 0 à au moins k-à-la-moins-k-ème puissance. Dans cette thèse, nous obtenons une condition suffisante pour les 3-graphes F qui satisfont π1(F) = 1/4. De manière intéressante, actuellement, tous les 3-graphes F connus dont π1(F) est de 1/4 satisfont cette condition. De plus, nous construisons également quelques 3-graphes intrigants F avec π1(F) = 1/4. Pour les k-graphes, nous donnons un cadre pour étudier πk-2(F) pour n'importe quel k-graphe F. En utilisant ce cadre, nous donnons une condition suffisante pour les k-graphes F satisfaisant πk-2(F) est k-à-la-moins-k-ème puissance, et nous construisons une famille infinie de k-graphes avec πk-2(F) est k-à-la-moins-k-ème puissance. En 2016, Lenz et Mubayi ont posé le problème de caractériser les k-graphes F tels que chaque k-graphe H suffisamment grand (d, μ, dot)-dense avec d > 0, v(F)|v(H) et un degré minimum de sommet positif contient un F-facteur. Motivés par ce problème, nous démontrons un théorème général sur les F-facteurs qui réduit le problème des F-facteurs de Lenz et Mubayi à un sous-problème naturel, c'est-à-dire le problème de F-cover. En utilisant ce résultat, nous répondons à la question de Lenz et Mubayi pour ceux F qui sont des k-graphes k-partis et pour tous les 3-graphes F, séparément. Dans le travail de Lenz et Mubayi, ils ont également construit une séquence de 3-graphes (1/8, μ, dot)-dense avec un degré minimum de sommet positif n'ayant pas de F-facteur, où F est un 3-graph k-parti complet équilibré. Dans cette thèse, nous prouvons que 1/8 est le seuil de densité pour garantir tous les 3-graphes 3-partis facteurs dans (d, μ, dot)-dense 3-graphes avec une condition de minimum degré de sommet Ω(n). De plus, nous montrons que l'on ne peut pas remplacer la condition de minimum degré de sommet par une condition de minimum degré de sommet. En particulier, nous étudions le seuil de densité optimal des F-facteurs pour chaque 3-graph 3-parti F dans (d, μ, dot)-dense 3-graphes avec un minimum degré de sommet Ω(n). De plus, nous étudions également les problèmes de F-facteurs pour les k-graphes k-partis F avec une hypothèse quasi-aléatoire plus forte et un minimum degré de sommet positif
Given a k-graph (k-uniform hypergraph) F, the Turán density π(F) of F is the maximum density among all F-free k-graphs. Determining π(F) for a given k-graph F is a classical extremal problem. Given two k-graphs F and H, a perfect F-tiling (or F-factor) of H is a collection of vertex-disjoint copies of F in H that together cover all the vertices of H. Perfect tiling problems, as a strengthening of the Turán problem, aim to find extremal conditions on H which guarantee an F-factor, which also has a long and profound history. In this thesis, we use many powerful tools including the probabilistic method, hypergraph regularity method and absorbing method to study Turán densities and perfect tilings of given k-graphs F in uniformly dense hypergraphs. Unlike graphs, we all know that there are several non-equivalent notions of quai-randomness in k-graphs for k ≥ 3. Hence, our work also has several non-equivalent definitions of uniformly dense k-graphs. Roughly speaking, a k-graph H is (d, μ, ⋆)-dense means that it is d-dense and ⋆-quai-randomness for some small μ > 0 with respect to given random structures. Restricting to (d, μ, 1)-dense 3-graphs, the Turán density of a given 3-graph F is denoted by π1(F). Determining π1(F) was suggested by Erdős and Sós in the 1980s. In 2018, Reiher, Rödl and Schacht extended the concept of (d, μ, 1)-dense 3-graphs to (d, μ, k-2)-dense k-graphs for k ≥ 3, and they proposed the study of uniform Turán density πk-2(F) for a given k-graph F in (d, μ, k-2)-dense k-graphs. In particular, they showed that πk-2(•) “jumps” from 0 to at least k-to-the-minus-kth-power. In this thesis, we obtain a sufficient condition for 3-graphs F which satisfy π1(F)= 1/4. Interestingly, currently all known 3-graphs F whose π1(F) is 1/4 satisfy this condition. In addition, we also construct some intriguing 3-graphs F with π1(F) = 1/4. For k-graphs, we give a framework to study πk-2(F) for any k-graph F. By using this framework, we give a sufficient condition for k-graphs F satisfying πk-2(F) is k-to-the-minus-kth-power, and construct an infinite family of k-graphs with πk-2(F) is k-to-the-minus-kth-power.In 2016, Lenz and Mubayi posed the problem of characterizing the k-graphs F such that every sufficiently large (d, μ, dot)-dense k-graph H with d > 0, v(F)|v(H) and positive minimum vertex degree contains an F-factor. Motivated by this problem, we prove a general theorem on F-factors which reduces the F-factors problem of Lenz and Mubayi to a natural sub-problem, that is, the F-cover problem. By using this result, we answer the question of Lenz and Mubayi for those F which are k-partite k-graphs and for all 3-graphs F, separately. In the work of Lenz and Mubayi, they also constructed a sequence of (1/8, μ, dot)-dense 3-graphs with positive minimum vertex degree having no F-factor, where F is a balanced complete 3-partite 3-graph. In this thesis, we prove that 1/8 is the density threshold for ensuring all 3-partite 3-graphs perfect tilings in (d, μ, dot)-dense 3-graphs given a minimum codegree condition Ω(n). Moreover, we show that one can not replace the minimum codegree condition with a minimum vertex degree condition. In particular, we study the optimal density threshold of F-factors for each 3-partite 3-graph F in (d, μ, dot)-dense 3-graphs with minimum codegree Ω(n). In addition, we also study F-factor problems for k-partite k-graphs F with stronger quasi-random assumption and positive minimum 1-degree